photomaster - phys8 - from quanta to quarks

8/18/2019 PhotoMaster - Phys8 - From QUANTA to QUARKS

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HSC Physics Option Topic “From Quanta to Quarks”Copyright © 2006-2009 keep it simple sciencewww.keepitsimplescience.com.au

keep it simple science

®

1

HSC Physics Option Topic

From QUANTA to QUARKS

What is this topic about?To keep it as simple as possible, (K.I.S.S.) this topic involves the study of:1. RUTHERFORD & BOHR MODELS OF THE ATOM

2. DE BROGLIE & MATTER WAVES

3. INTO THE NUCLEUS

4. APPLICATIONS OF NUCLEAR PHYSICS

...all in the context of the history, nature and practice of Physics.

1. RUTHERFORD & BOHR MODELS OF THE ATOM

What Has Gone Before...The entire Science of Chemistry and much of Physics is built on the foundation of AtomicTheory... the concept that all matter iscomposed of atoms.

Initially conceived as tiny, unbreakable particlesof matter, by the beginning of the 20th century itbecame apparent that the atom was composedof smaller parts.

In 1900, Max Plank had proposed the QuantumTheory to explain the details of the “ Black BodyRadiation Curves” .

In 1905, Einstein then explained the strangephenomenon of the Photoelectric Effect byusing Plank’s quantum idea. He proposed thatlight i s not just a wave, nor a stream of particles,

but made up of “wave packets” .

Einstein also proposed his “ Theory of

Relativity” in 1905. Classical Physics was beingturned upside-down by this sequence of new,fundamental d iscoveries.

The Rutherford Model of the AtomIn 1911, Ernest Rutherford carried out anexperiment which indicated that the positivelycharged part of an atom must be concentratedinto a tiny “ nucleus” , with the electrons orbitingaround it.

Rutherford’s modelproposed that:• At the centre is a tiny, dense nucleus with a

positi ve electrical charge.• The negatively charged electrons orbit around

the nucleus.• The distance from nucleus to the electron

orbits is very large compared to the size of the

particles, so the atom is mostly empty space.

Since negative charge was carried by particles(the electrons) Rutherford thought it likely thatthe nucleus was made of posit ive particles.These were soon called “ protons” and their existence was confirmed a few years later.

The electrons were too light to account fo r muchof the mass of an atom, so he thought theprotons must be relatively heavy.

Even at this early stage there was speculationthat there might be another massive particle inthe nucleus as well, but its discovery had to wait20 years.

In his famous experiment withcathode rays, J.J.Thomson had

discovered the (negatively charged)electrons in all atoms.

This meant that there also had tobe a positive part of each atom.

Light is NOT a stream of particles...

Light is NOT a wave...

Light is a stream of “wave packets”... “PHOTONS”

Each photon is both a particle AND a wave!

Rutherford’s

ATOM

Electrons in orbitaround central

nucleus

Atom mostlyempty space

Nucleus of positivelycharged matter,

possibly made up ofof particles

+

+

+

+

--

-

-


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2

Problems with Rutherford’s AtomEven as he proposed his atomic model, Rutherfordknew there was a problem with it.

The existing theory of Electromagnetic Radiation(EMR) contained the concept that if an electricallycharged particle was accelerating, then it must emitEMR, in the form of light waves.

Since Rutherford’s electrons were imagined to be incircular orbits around the nucleus, and since circular motion involves constant (centripital) acceleration,then it follows that each electron should beconstantly emitting l ight. Trouble is... they obviouslydon’t!

Existing accepted theory required that an orbiting electron should emit light energy continuously.

Obviously they don’t, or all matter would

constantly glow with light.

However, atoms DO emit light if stimulated with energy, such as in a high-voltage discharge tube.

Emission SpectraYou should be familiar with the idea of a“ spectrum” of light. For example, if “ white” lightis passed through a prism, the differentwavelengths are separated, and the familiar rainbow colours appear.

(use your imagination...

we can’t print colours)

If the light emitted by atoms of aparticular element is put through a prism, thespectrum shows very narrow bright lines on adark background because only certainwavelengths are given out. The pattern of linesis characteristic for each element.

Red

Orange

Yellow

Green

Blue

Violet

white light isa mixture of wavelengths

differentwavelengthsspread out to

form a spectrum

ElementA

ElementC

ElementB

Practical Work

Emission Spectrum of HydrogenYou will have observed the emission spectrumfor hydrogen by using a spectrometer to view thelight from a discharge tube fil led with low-pressure hydrogen gas.

You will have seen that the light f rom a hydrogendischarge tube is composed of 4 visible brightlines of light.

Each line is one single wavelength of l ight.

High Voltagefrom induction coil

Tube glowswith emittedlight

Spectroscope

Slit & lensPrism Optical

viewing system

“Telescope” can berotated to view thedifferent “lines” of theemission spectrum

T u b e f i l l e d

w i t h H y d r o g e n g a s

The Balmer Series &Rhydberg Equation

The lines in the emission spectrum of hydrogenhad been discovered some 20 years beforeRutherford’s work, and were known as the“ Balmer Series” .

Each l ine was g iven a name (Hα, Hβ, Hχ & Hδ) andthe precise wavelength of each had beenmeasured. Other similar series of lines wereknown to exist in the invisible infra-red and ultraviolet parts of the EMR spectrum.

No-one could explain them, but mathematiciansBalmer and (later) Rhydberg had worked out thatthe exact wavelengths of the hydrogen spectrumlines could be calculated from an empiricalequation:

The fact that the Rhydberg equation worked was strongevidence that there was an underlying “ law” controllingthe hydrogen spectral lines. The fact that a series of integer numbers were involved was a clue that

connected the whole thing to Plank’s Quantum Theory...

The Rhydberg Equation

1 = RH( 1/nf 2 - 1/ni

2 )λ

λ = wavelength of the spectral line (in metres)RH = the “Rhydberg constant” = 1.097 x 10

7

nf = an integer number. For the Balmer series n f = 2ni = an integer number. To calculate the wavelengths

of the 4 lines of the Balmer series, n i takes thevalues 3, 4, 5 or 6.

Each line islight of oneexact wave-

length.

Light is onlyemitted at

certain

precise

wavelengths

Each

element

has its ownunique setof spectral

lines

lightemission

fromelectrons


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3

Plank’s Quantum Theory A quick revision of what you learned previously...

In 1900, Max Plank proposed a radical new theoryto explain the black body radiation. He found thatthe only way to explain the exact details comingfrom the experiments, was that the energy wasquantised: emitted or absorbed in “ little packets”called “quanta” (singular “quantum”).

The existing theories of “classical” Physicsassumed that the amount of energy carried(say) by a light wave could have any value, on acontinuous scale. Plank’s theory was that theenergy could only take certain values, based on“ units” or quanta of energy.

Plank proposed that the amount of energy carriedby a “quantum” of light is related to the frequencyof the light, and can be calculated as follows:

Neils Bohr Puts It All Together Bohr used Plank’s Quantum Theory to modify theRutherford model of the atom in such a way that:

• the problem of radiation that should be emittedconstantly from accelerating electrons wasovercome.

• the underlying reasons for emission spectra were

explained.• the empirical nature of the Rhydberg Equation was

given theoretical backing and mathematical validity.• the reasons for the “ valency” of different atoms, and

how and why they combine in f ixed ratiosbecame clearer.

Not bad for an afternoon’s work!

(The last point above is fundamental to Chemistry andunderstanding chemical bonding and formulas. It willnot be pursued any further in this topic)

Bohr ’s Postulates• Electrons revolve only in certain “ allowed” o rbits.

Bohr theorised that there are a series of orbits, atfixed distances from the nucleus, in which an electronwill not constantly emit radiation as demanded byclassical theory.(Why was explained later by de Broglie)

• Electrons gain or lose energy to “jump” betweenorbits. To jump up to a higher orbit, an electron mustgain a certain quantity of energy. If it drops back tolower orbit, it must emit that exact same amount of energy.

These quantities of energy are “quantised”, so eachorbit is really a “ quantum energy level” within theatom.

The amount of energy absorbed or emitted during a“ jump” is defined by Plank’s Equation E = hf, and thecorresponding wavelengths of light are defined bythe Rhydberg Equation. The integer numbers n f and n iturn out to be the “quantum numbers” of the orbits,counting outwards from the nucleus.

• Electrons in “ allowed orbits” have quantised amountsof angular momentum too.

Bohr figured out that the amount of angular momentumpossessed by an electron must always be a multiple of h/2π. The significance of this will be dealt with in a later

section.


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E = h.f

E = energy of a quantum, in joules ( J)h = “ Plank’s constant ” , value 6.63x10

-34

f = frequency of the wave, in hertz (Hz)

You are reminded also, of the wave equation:

V = λ .f (or, for light) c = λ .f

c = velocity of light (in vacuum) = 3.00x108ms

-1.

λ = wavelength, in metres (m).f = frequency, in hertz (Hz)

Example Calculationa) Use the Rhydberg Equation to find thewavelength of the Hδ line of the hydrogenspectrum, given that nf = 2 and ni = 6.

1 = RH( 1/nf 2

- 1/ni2

)λ

= 1.097x107( 1/2

2- 1/6

2)

1/λ = 2.438 x 106

∴ λ = 4.10x10-7 m (410 nm nanometres)

b) Use the “Wave Equation” to find thefrequency.

c = λ .f 3.00x10

8= 4.10 x10

-7x f

∴ f = 3.00x108/4.10x10

-7

= 7.32x1014

Hz.

c) Use Plank’s Equation to calculate theenergy carried by one photon of light in the Hδspectral line.

E = h.f = 6.63x10

-34x 7.32x10

14

= 4.85x10-19

J.

“ Allowed” orbitpositions.

Electrons cannot orbitanywhere else.

Electrons can “jump”from one orbit toanother, but must

absorb energy to jump

higher, or emit energyto drop lower.

Quantum numbers of the orbits.

1

2

3


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Bohr & the Balmer SeriesLet’s see how Bohr’s ideas work with regard to theBalmer Series of hydrogen emission lines.

Bohr suggested that the Hα emission line was due toan electron dropping from the 3rd orbit down to the2nd orbit. It must lose a precise quantum of energy,so it emits a photon of light at a precise frequency

given by E = hf.

In the Rhydberg Equation, n i = 3 and nf = 2. Thecalculated wavelength (λ ) agrees perfectly with theobserved spectral line. Plank’s Quantum Equationcalculates the energy of that photon of light.

Bohr argued that this amount of energy mustrepresent the difference in energy level from orbit 2to orbit 3.

The other lines of the Balmer Series representelectrons dropping from higher orbits into the 2ndorbit:

It all worked! Bohr’s idea gave a theoreticalexplanation for the Rhydberg Equation, which hadbeen empirically derived to explain the observedspectral lines.

Limitations of theRutherford-Bohr Model

Despite the way that Bohr’s Postulates seem to solvethe problem with Rutherford’s brilliant new concept of the atom, there were still unexplained difficul ties.

Bohr Model worked only for Hydrogen

Hydrogen is the simplest atom, with only oneelectron and one proton.

At tempts to apply the model to larger atomsfailed, because multiple, orbiting electronsinteract with each other as well as the nucleus,and the situation becomes too complex todescribe in a simple mathematical way.

Different Intensities of Spectral LinesThe different spectral lines showed differentintensities or brightness. This means that someorbital “ jumps” by electrons always occur moreoften than others. Bohr’s model had no

explanation as to why.

“ Hyperfine” Spectral LinesWhen the spectral lines were examined moreclosely, each one was found to be made up of anumber of very f ine lines close together.

The Zeeman EffectWhen a discharge tube i s operated within a magneticfield, each spectral line is split up into severalseparate lines.

This, and the presence of the “hyperfine lines”,suggested that the energy levels or orbits weredivided into a number of “sub-orbits” of slightlydifferent energy. Bohr’s model had no explanation for this.

Like all scientific models, the Rutherford-Bohr atomis a human attempt to explain the observed facts of nature. In its day, this model was the best explanationavailable, but it was recognised that certain factsremained unexplained.

This doesn’t make the model wrong... simplyincomplete. It was a “ work-in-progress”, to be addedto and refined by later scientists. This is the wayScience works.

If further evidence had proven it totally wrong (as canhappen) you would no t be studying it!

1

2

3

4

5

6

Hδ line. ni = 6

Hχ line. ni = 5

Hβ line. ni = 4

Hα line. ni = 3

light photon emitted

+

Quantum energylevels or “allowedorbits” around thehydrogen atom

Nucleus

n

f = 2

in each case

The Hydrogen Spectrum &Development of Bohr’s Model

Without a knowledge of the emission spectrum of hydrogen, it seems very unlikely that Bohr could havecome up with his idea.

The fact that the spectrum shows distinct lines, andthat integer numbers are involved in the RhydbergEquation, all pointed to some kind of discrete,quantised atomic arrangement, rather than the more-or-less random orbits of Rutherford. Withoutknowledge of the hydrogen spectrum, (and Plank’sQuantum Theory) Bohr could not have made the(literally) quantum leap to his idea.

Like all great scientists, Bohr built on the knowledgediscovered by others. His genius was to put it alltogether in a new synthesis, that helped establishRutherford’s new structure of the atom.

However, there were still some problems...

Increasing energy

dif ference giveshigher frequency

(and shorter wavelength)of spectral light

M a g n i f i e

d v i ew

Spectral lines are ofdifferent brightness

Spectral lineis made up ofa number ofseparate,

finer lines

Hα line. ni = 3 )

Hβ line. ni = 4 )Hχ line. ni = 5 )Hδ line. ni = 6 )


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1.Sketch a labelled diagram to show the mainfeatures of Rutherford’s atomic model.

2.Outline the major problem with Rutherford’satomic model, based on the accepted theory of that time.

3.a) What is the “ Balmer Series” ?

b) Calculate the wavelength of the Hβ spectralline for hydrogen, given that n i = 4 and nf = 2.

c) Use the wave equation, and Plank’s equationto find the amount of energy carried by onephoton of the Hβ line.

d) According to Bohr, what does this amount of energy represent with in a hydrogen atom?

4. Analyse the sign if icance of the hy drogenspectrum in the development of Bohr’s atomicmodel.

5.The Hχ spectral line for hydrogen is due to anelectron dropping from the 5th to the 2nd orbit.

Compared to the Hβ line (in Q3):a) would a photon of the Hχ line carry more, less,or the same amount of energy? Explain.

b) would the Hχ line have a higher, lower, or thesame frequency? Explain.

c) would the Hχ line have a longer, shorter, or the same wavelength? Explain.

6.a) List, in brief form, 3 of “ Bohr’s Postulates” .

b) List, in brief form, 4 limitations of the Bohr model.

7.It is known that other spectral lines for hydrogenare present in the infra-red and ultra-violet partsof the spectrum. One line, for example, is due toelectrons dropping from the 8th to the 1st orbit.

Calculate the wavelength of this spectral lineand state if it is inf ra-red or ultra violet.

5


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Summary Worksheet for Section 1 is at the end of the next section

Worksheet 1 Test Questions section 1 Student Name...............................


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de Broglie’s Quantum ProposalRemember that in 1905 Einstein had explainedthe Photoelectric Effect by suggesting that lighthas both wave and particle properties. (For thishe was awarded the Nobel Prize)

Einstein had used Plank’s Quantum Theory toexplain a phenomenon that “c lassical” Physicswas unable to explain.

In 1924, a young graduate student Louis deBroglie turned this concept around...

If light waves can have particle-like

properties, why can’t particles havewave-like properties?

Using Quantum Theory and Bohr’s atomicmodel, de Brogl ie developed a mathematicalmodel for an electron in orbit around thenucleus acting as a particle with waveproperties.

De Broglie began from Bohr’s equations whichshowed that (as a particle) the angular momentum of the electron would be a multipleof h/2π.

From this he was able to show that (whenshowing its wave properties) the electron wouldhave a wavelength related to its mass andvelocity:

Impact of de Broglie’s HypothesisDe Broglie’s proposals had almost no impact onthe scientific community at first. Hismathematics were checked and found to betotally correct. His hypothesis was totally

consistent with the Quantum Theory, and withthe Bohr model.

The physicists of the day, including Plank,Einstein, Rutherford and Bohr were all veryinterested by his work, but it was just a neatmathematical exercise, without any evidencebased in experiment or observation.

Usually, scientists observe a phenomenon andthen try to explain it by theory. de Broglie wasputting theory first, without any facts to explain!

Eventually, (as happens in Science) anexperiment was done to test the hypothesis.Before learning about that, you need tounderstand an important wave phenomenon...

DiffractionWaves can undergo various “ wave phenomena”such as reflection, refraction and interference.In fact, it is these things which can identifywaves. For example, it was interference whichallowed Hertz to prove the existence of invisibleradio waves back in the 1880’s.

Diffraction is something that only waves do.

You can see diffraction occur i f you watch water waves enter a harbour or similar.

At th is point you might th ink “ so what?”The “so what” is what happens AFTER

diffraction occurs...

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2. DE BROGLIE & MATTER WAVES


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Light is a stream of “wave packets”... “PHOTONS”

Each photon is both a particle AND a wave!

λ = hmv

λ = wavelength (metres) of the electron.h = Plank’s constant (= 6.63x10

-34)

m = mass of the electron (= 9.11x10-31

kg)v = velocity of the electron, in ms

-1.

Example CalculationFind the wavelength of an electron which is

travelling at a velocity of 4.35x105

ms-1

.

Solutionλ = h

mv= 6.63x10

-34/(9.11x10

-31x 4.35x10

5)

= 1.67x10-9

m (1.67 nanometres)

Barrier with gaps in it

The part of thewave which getsthrough a gapwill act like a

point source ofwaves. A semi-circular wavepattern forms

from each gap.

This is Diffraction

Parallel wavefrontsapproach thebarrier.

Most of thewave energywill beabsorbed orref lected.


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7

Diffraction FormsInterference Patterns

Once a set of waves have been diffracted, the 2(or more) sets of spreading waves now meeteach other and wave interference occurs:

If light waves are diffracted, then projected ontoa screen, or captured on photographic film, aninterference pattern appears... perhaps a line of light spots (where waves add together constructively) and dark zones (where wavesare cancelling). The exact appearance of thepattern depends on the geometry of the “ slits”and the wavelength of the waves.

Davisson & Germer’s ExperimentDavisson and Germer used a modified cathode raytube to test de Broglie’s hypothesis.

A beam of electrons travell ing through a vacuum wasallowed to strike a crystal of nickel, speciallyprepared so that electrons wou ld reflect from parts of it. Different parts of the beam could then overlap their

pathways as they travelled into a detection devicewhich cou ld measure the intensity of the beam.

Result? An in terference pattern was detected! This provedthat electrons have wave properties, and confirmedthe de Broglie hypothesis.

Why Are the Bohr Orbits Stable? A quick review o f some important points:

Rutherford’s atomic model places electrons in orbit,but classical theory predicts they should constantlybe emitting light because they are accelerating.

However, this isn ’t happening, so Bohr p roposes thatthere are “allowed” , stable orbits where electronsdon’t constantly give off light. (They only radiatewhen they “ jump” orbits)

What makes these “allowed orbits” stable?

de Broglie’s particle-wave theory of the electronexplains:

An allowed orbit is where the wavelength of theelectron exactly fits to form a “ standing wave”around the nucleus.

“ Standing waves” are a well-known wavephenomenon in which an exact number of fullwavelengths can “ resonate” or reverberate in astable way. For example, all musical inst rumentsinvolve standing waves of sound energy in astring or air space.

The “allowed orbits” around an atom are locatedat distances from the nucleus which allow thequantum energy of the electron to fit in an exactnumber of wavelengths to form a standing wave.

At any other distance, the orbit cannot fi t astanding wave with an exact number of wavelengths, so the electron cannot exist there.

The electron is a particle, with mass andmomentum. It is also a wave, with a wavelength(λ = h/mv) and capable of diffraction,interference and standing wave behaviour.

Welcome to the world of Quantum Physics!


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+

+

=

If the waves are “in phase” (crest matches crest) thewaves add together for double the amplitude

If the waves are “out of phase” (crest matchestrough) the waves cancel for zero amplitude

Constructiveinterference

Destructiveinterference

Light falling onscreen or photo filmshows a pattern of

light and dark spots

Light spotwhere wavesadd together

Dark zonewhere wavescancel

Diffracting waves formInterference Patterns

Can you guess what’s coming?

de Broglie has proposed an hypothesis thatelectrons may have wave properties.

What should a good scientist do?Test the hypothesis by experiment, of course!

How do you test for wave properties?Test electrons to see if they show

Diffraction & Interference Patterns, of course!

Beam of light striking abarrier with slits in it

An electron

forms a“Standing

Wave”

around thenucleus

+


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8

The Contributions of Heisenburg & PauliBefore you leave the electron o rbits and dive into the atomic nucleus,

the syllabus asks you to assess the contributions of 2 other great scientists.

Werner Heisenberg (1901-76)was a German physicist who is best

remembered for the“ Heisenberg Uncertainty Principle” ,

for which he was awarded theNobel Prize in 1932.

Heisenberg developed the mathematicalframework for Quantum Mechanics. He showedthat the dual nature of the “ particle-wave” which

describes the electron (and the l ight photon),makes it impossible to know everything aboutany particle at any moment. Either you know

where it is, or you know how much momentumit has, but you cannot know both things at once

with any certainty.

This “uncertainty” about things at the atomicscale was described by Heisenberg as

mathematical probabilities. Thus an electronorbit becomes a “ region of probability” in which

there is a good chance (but not a certainty)that the electron exists.

This all sounds very airy-fairy, but its validityhas been spectacularly confi rmed by manyexperiments and phenomena such as the“quantum tunnelling” effect, involved insemiconductor operation and electrical

superconductivity.

Wolfgang Pauli (1900-58)was born in Austr ia, but became an American

citizen. He is best remembered for the“ Pauli Exclusion Princip le” , (Nobel Prize 1945)

which states that 2 electrons in the sameatom cannot have exactly the

same quantum state.

His mathematical analysis established theidea that the Bohr-de Broglie orbits are justone of several dif ferent types of quantum

properties that electrons can have.

This gives rise to the idea of “ sub-orbits”within an atom (this explains the “hyperfinelines” in emission spectra) and shows why 2

electrons with almost the same quantumstate, but opposite “ spin”

will tend to pair up. (Hence “ Cooper Pairs” ,and electron pairs in chemical bonding.)

Later in this topic you will see that Paulialso made an important contribution

to understanding nuclear processes as well.

An AssessmentIn the 1920’s, Quantum Theory was being accepted as a “necessary evil” to

satisfactorily describe the structure of an atom, and

account for all the known observations.However, the explanations being used were a mixture of new “ quantum” ideas

overlaid on a framework of “ classical” Physics, so it was all ratherartificial or contrived.

It was the theoretical work of Heisenberg & Pauli that built QuantumMechanics into a complete, new branch of Physics wi thout the

need for any reference to the “old” Physics.

Therefore, their contributions must be seen as being very important. Although the details of their work are beyond the scope of th is course, theyallowed Physics to become a fully modern study with a complete theoreticalbase which can explain atoms, super-conductiv ity, semi-conductors , nuclear

processes and even the creation of the Universe itself.

“If you think you understandQuantum Theory...

then you really don’tunderstand Quantum Theory ”


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COMPLETED WORKSHEETS

BECOME SECTION SUMMARIES


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Worksheet 2 Rutherford-Bohr Model of the AtomFill in the blank spaces Student Name..........................................

Worksheet 3 de Broglie & Matter WavesFill in the blank spaces Student Name..........................................

• Electrons can q).............................. from oneorbit to another. When they do so they mustr)............................ or ..................................... anamount of energy. This energy difference

relates to the s)................................ of a spectralline in accord with t)...........................’s QuantumTheory and the u).................................. equation.• Electrons in “ v)............................... orb its” havea quantity of w)...................................... which isalways a mult iple of h/2π.

Bohr was able to link his idea to the Balmer Series of hydrogen spectral lines. In fact, it ishighly unlikely he could have developed hisidea without this evidence.

However, the Bohr model had a number of limitations:• It worked only for x).............................................• It could not explain the differenty)...................................... of the spectral lines.• There was evidence from the “ z).........................Effect” , and the observed “ aa).............................”spectral lines, that each orbit was actuallyab)......................... ..................................................The model could not explain theseobservations.

Rutherford’s model of the atom:• in the centre is a tiny, dense a).............................• Electrons (discovered by b)................................)

are in c)................................ around the outside.The model had a major problem: theoretically,

electrons which are d)................................ shouldconstantly emit e)...................................., causingall matter to constantly f)....................... with l ight .

The “ g).......................................................” of anelement refers to the precise set of h).................................... of light emitted if theelement is energised, for example, in ai).............................................................. The linesare visible if the light is viewed through a j)...................................................

The visible lines in the spectrum of k)................................. had been named the“ l)................................. Series” , and them)........................................ equation had beenformulated to calculate the n).................................of each of the lines in the series.

Bohr used the evidence of the Balmer Series to refine

Rutherford’s atomic model. He suggested that:

• Electrons o).........................................................,in which they will not p).........................................

Louis de Broglie argued that if Einstein’sphotons of light are waves with a)........................properties, then electrons could beb)....................... wi th c)....................... properties.

He extended Bohr’s model to derive an equationfor the d).............................. (wave measurement)of the electron. Bohr’s “ allowed orbits” wereexplained as e)....................................... waves,

with an integer number of f)..................................fitting exactly around that orbit.

De Broglie’s hypothesis had g)..............................impact on the scientific community. It seemedan interesting idea, but there was noh)............................... from observations or i)................................... to connect it to.

Two scientists, j)........................... &............................ carried out an experiment inwhich a beam of k)............................... was aimedat a crystal.

They detected an l).............................. patternwhich proved that the electrons wereundergoing m)................................. This provedthat electrons do have n)..................... properties,and confirmed de Broglie’s hypothesis.

o).............................. is a wave phenomenon inwhich waves which penetrate a small aperture,then act like a point source of waves andp)........................ in a q)..........................................pattern. When waves from 2 (or more) aperturesoverlap, they r).................................... with eachother. Where crest meets crest the wavess)................... ........................... creating a higher t).................................... wave. Where crest meetstrough, the waves u)........................ each other.With light, this results in a pattern of v)......................... and ................................. spots.

Following the confirmation of de Broglie’stheory, the science of Quantum Mechanics wasgiven a complete theoretical framework by thework of Werner w)....................................... and

Wolfgang x)...............................


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1.Use de Broglie’s equation to calculate:a) the wavelength of an electron with velocity2.25x10

6ms

-1(mass of electron = 9.11x10

-31kg)

b) the velocity of an electron if its quantumwavelength is 4.75x10

-9m.

c) Use the wave equation to find the quantumfrequency of the electron in (b).

d) Use Plank’s equation to calculate thequantum energy of the electron in (b).

2.Describe the impact of de Broglie’s proposalthat particles could have wave properties. Ac count for th is reaction by the sc ient if iccommunity.

3.Outline the experiment of Davisson & Germer.State the result of the experiment and explainthe significance of this result.

4.Explain how de Broglie would describe Bohr’s“ allowed orbits” around the nucleus.

5.a) What is di ffraction?

b) The diagram shows a breakwall with parallelwater waves approaching. There are 3 boatchannels through the wall. Complete the

diagram showing the pattern of the waves whichgo through the boat channels.

6. Assess the contribution of Heisenberg & Paulito the development of atomic theory.

Water waves striking abreakwall with 3 boat channels


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Nucleons A “ nucleon” means any par ti cl e locat ed in thenucleus of an atom. We now know that there are 2types of nucleon:

ProtonsThe existence of protons was considered likelyalmost as soon as the electron was discovered. Bythe 1920’s the proton had been positively identified,and its properties measured.

Neutrons As early as 1907 i t had been suggested that protonsalone were not sufficient to account for the mass of most atoms. It was suspected that there must beanother nucleon, with considerable mass, but noelectric charge. However, it was 25 years before theneutron’s existence was proven.

Contrasting the Properties of the Nucleons

Proton Neutron

Electrical

Charge +1.602x10-19

C 0 (neutral)

Mass 1.673x10-27

kg 1.675x10-27

kg

Note that:• The charge on a proton is exactly the samemagnitude, but of opposite sign to that carried by anelectron.

• In a normal atom:No. of protons = No. of electrons = “ Atomic No.”

• Protons and neutrons have almost identicalmasses. (The neutron is slightly heavier)

Both are almost 2,000 times heavier than an electron,so virtually all the mass of an atom is in the nucleus.

No.protons + No.neutrons = “Atomic Mass Number”

For example:Sodium atom

electrons = 11protons = 11

neutrons = 12

Total nuc leons = 23(protons + neutrons)

Atomic Mass Number = 23

Atomic Number = 11

Discovery of the NeutronThe existence of the neutron was proven in 1932by James Chadwick (1891-1974).

It was impossible then to detect and measure

neutrons directly. The method Chadwick usedrelied upon neutrons colliding with other particles, then applying the scientific principlesof Conservation of Energy and Conservation of Momentum to measure the properties of theneutron.

• The alpha (α) particles emitted by a radioactivesubstance were used to bombard a berylliumtarget.

• The beryllium emitted neutrons, which (havingno electrical charge) are very penetrating andare unaffected by electric or magnetic fields, socould not be measured or studied directly. Other scientists had thought the radiation was gamma( γ ) waves of extreme high energy.

• Some of the neutrons then hit a second targetof paraffin wax, which has a lot of hydrogen in it.Occasionally a neutron colli sion would dis lodgea proton.

• Chadwick was able to study some of theseprotons and measure the energy they carried.

• Chadwick could then apply the principles of Conservation of Momentum and Energy tocalculate the mass and velocity of whatever hadhit the protons and dislodged them.

The results indicated the presence of a particle(not γ -rays) with a mass almost the same as aproton, and no electric charge. This matchedperfectly with the (then hypothetical) neutron,so the existence of the “missing” nucleon wasconfirmed.

11

3. INTO THE NUCLEUS


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Thus we get the familiar atomic model, withelectrons (in Bohr’s allowed orbits) around a

nucleus of protons and neutrons.MAKE SURE YOU UNDERSTAND THE SHORTHAND DESCRIPTION

Na

3

11

α n0

p

+

Berylliumtarget

Paraffin Waxtarget

Radioactivesubstance

emittingα-particles

Detectingequipment

Background InformationRadioactivity had been discovered in 1896.

Although it was not fully understood, the use ofα-particles as “atomic bullets” in experiments

had become quite routine.

After Chadwick’s experiment, the neutron

became the next “bullet” of choice.


12/32


13/32




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13

It was known that the electrons ejectedduring Beta decay varied considerablyin their velocity, and the amount of energy they carried. This was puzzling,because it was thought that the processinvolved was the same in every β-decay,so why did the energy vary?

In 1931, Wolfgang Pauli suggested aquantum explanation.

What if there was another particle beingproduced, that no-one had detected?This “missing” particle could carryaway some of the energy in varyingamounts.

n

neutron

proton

anti

neutrino

β-particle(electron) -

The sum of theenergy of the beta

particle andneutrino alwaysadds up to thesame amount.

What Holds the Nucleus Together?

This question had been asked as soon asRutherford had proposed that atoms have anucleus. There were just 2 forces then understood,which could be operating in the nucleus:

Gravity Al l masses att ract all other masses by gravity.

This would attract all nucleons to each other.

Electrostatic Forces Al l charged part ic les exert a force on other charged particles. This force would not act onneutrons, but should cause protons to berepelled by other protons.

Calculations showed that theelectrostatic repulsion would be much,

much s tronger than gravity. Thenucleus should instantly fly apart!

Since the nucleus does exist, and doesn’tinstantly explode, it was realized that there mustbe another force operating. It was called simplythe “ Strong Nuclear Force” .

Its properties could be inferred and calculated:• It must be much stronger than the proton-

proton electrostatic repulsion. (it’s over 100Xstronger)

• It must be independent of charge and attractall nucleons... protons & neutrons.

• It must be extremely short-ranged, operatingonly across the tiny di stances of the nucleus.(Otherwise it might cause neighbouring atomicnuclei to fuse together, and eventually pull allmatter into one lump!) Even before its existencewas proven, the Strong Nuclear Force wasknown to exist, and scientists began

speculating on how to tap into its enormousenergy potential...

To have avoided detection, this hypotheticalparticle must have no mass (or so little that itwas not measurable) and no electric charge.However, it could carry quantum energy. Pauli’sidea was that there was a certain total energyinvolved in b-decay; some was carried off by thebeta particle, the rest by the mystery particle.

Enrico Fermi did the mathematics andthe whole scenario worked so well intheory that the scientific communityaccepted the new particle, even thoughit was not positively detected andidentified until 1956.

This new particle was eventuallychristened the “neutrino” (little neutral

one) and is now a totally accepted factof the sub-atomic quantum world. Infact, there are a whole family of neutrinos; to keep it simple (KISSPrinciple!) the one released in betadecay is an “anti-neutrino” .

The symbol used for the anti-neutrino is ν. The full equation for a beta decay istherefore:

Pauli and the Neutrino

6

14

C-1

+

+

0

e-

7

14

N

Carbon Nitrogen

anti-neutrino

Gammaβparticle

γ ν


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14

Mass Defect in the NucleusIt was realized that incredibly powerful forceswere operating within the atomic nucleus. Howcould such forces arise?

The answer lies in the fact that the mass of every atomic nucleus (except hydrogen ) DOESNOT ADD UP.

This difference is called the “ Mass Defect” . It’sas if a little bit of mass “ went missing” when theprotons and neutrons joined together to formthe nucleus.

Where is the missing mass?

It has converted to energy...

(you should have knownthat Einstein would be

involved sooner or later!)

...to provide the “Binding Energy” of the StrongNuclear Force which holds the nucleustogether.

Einstein had developed his most famousequation as part of his Theory of Relativity. He

never anticipated that it would find another use...

Measuring Mass & Energy in the NucleusBefore going any further, you need to know about the commonly used methods of

measuring mass and energy at the atomic level.

Mass in Atomic Mass UnitsThe “ atomic mass unit” (u) is a measure of massdevised for convenience in Chemistry. Roughlyspeaking, both a proton and a neutron have amass of 1 u, although in the calculationsfollowing, you need to be much more precise.Obviously, 1 u is a very small mass:

1 u = 1.661x10-27

kg

You need to be able carry out calculations us ingeither unit, so the fol lowing data may be useful.

Proton Neutron

Mass (in kg) 1.673x10-27

1.675x10-27

Mass (in u) 1.0073 1.0087

Energy in Electron-VoltsThe “electron-volt” (eV) is an energy unit that isconvenient because the energy of sub-atomicparticles has traditionally been measured by their

behaviour within electric fields.

1 eV is the energy gained by an electron acceleratingin an electric field with a potential difference of 1 volt.

1 eV is an extremely small amount of energy:

1 eV = 1.602 x 10-19

joules of energy

so the unit often used is the mega-electron-volt(MeV)

1 MeV = 1x106

(one million) eV

This is convenient when dealing with individualatoms or particles.

If you add up the mass of all the

protons+neutrons in any nucleus,

the total is always more than the actual

measured mass of the whole nucleus.

Mass of Mass of Protons + Neutrons > Whole Nucleus

E = mc2

Example Calculation A normal carbon atom contains 6 protons and 6neutrons. (also 6 electrons, but mass is negligib le)The nucleus is known to have a mass = 11.9967 u

= 1.993x10-26

kgCalculate the Mass Defect,

and total Binding Energy.

SolutionIn kg and joules In u and MeV

Mass of 6 protons Mass of 6 protons= 6 x 1.673x10

-27= 6 x 1.0073

= 1.004x10-26

kg = 6.0438 u

Mass of 6 neutrons Mass of 6 neutrons= 6 x 1.675x10

-27= 6 x 1.0087

= 1.005x10-26

kg = 6.0522 uTotal particle mass Total particle mass

= 2.009x10-26

kg = 12.0960 u∴ Mass defect ∴ Mass defect= 2.009x10

-26- 1.993x10

-26= 12.0960 -11.9967

= 1.600x10-28

kg = 0.0993 u

This missing mass has Each 1 u converts toconverted to bind ing 931.5 MeV of energyenergy according to (This value is in your

Physics Data Table)E = mc

2So, binding energy

= 1.6x10-28

x (3.00x108)2

= 0.0993 x 931.5= 1.44 x10

-11J = 92.50 MeV

From here on, all calculations wi ll be done in

atomic mass uni ts (u) and MeV.

These are the same, justdif ferent units

These are the same, justdifferent units


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15

Nuclear FissionIn the 1930’s, it was discovered that bombarding“ target” atoms with alpha particles couldoccasionally produce a transmutation to a newradioactive isotope.

Aluminium α-particle new isotope neutronof phosphorus

In Italy, brilliant young physicist Enrico Fermi (1901-54) decided that using neutrons as “atomic bullets”would be even more productive.

In 1934 he began bombarding every possible element,in turn, with neutrons and studying the resultingradioactivity to detect any new radioisotopes. Over 40were discovered very quickly. For example:

In one experiment he bombarded uranium atoms withneutrons, confidently expecting to produce atoms of “transuranic” elements. The radiation “signatures”detected were unexpected and puzzling, but he wasfocused on other things and failed to investigatefurther.

Fermi had “split” the nucleus, but it was another 4years before other scientists in Germany confirmedwhat had happened. In his sample of uranium wereatoms of U-235 which had absorbed a neutron, then

totally disintegrated:

This is Nuclear Fission; the splitting of the nucleus.,with enormous energy release, due to a mass defectand E=mc

2.

Meanwhile, Fermi had continued on with his work,and was awarded the Nobel Prize of 1938 for hisproduction of new radioactive materials.

With war looming in Europe and a Fascist regime inItaly, Fermi and his Jewish wife used attendance atthe Nobel Prize ceremony in Sweden to flee to theUSA, where Fermi was immediately accepted into thescientific community.

By then he was aware of nuclear fission and its hugeenergy potential, and that the experiments confirmingfiss ion had been done in Nazi Germany. On the eve of World War II, it seemed that the knowledge to developan “ atom bomb” was in the hands of the enemy.

The Manhattan ProjectFollowing a “letter of concern” (outlining the danger of nuclear research in Nazi Germany) from Einstein tothe President of the USA , the top secret “ManhattanProject” was set up in 1942. Its objective was toresearch nuclear fission and develop an “atomicbomb” if this was possible.

The first step was to discover if a self-sustainingchain-reaction of fissions was possible. Enrico Fermiwas appointed the leader of the scientific team. Hedesigned the reactor or “nuclear pile”, which wasbuilt i n a squash court at the University of Chicago.

In December 1942 the reactor achieved the first self-sustaining, controlled chain reaction.

The Fission Chain ReactionSince fission is set off by a neutron, and since itreleases more neutrons, it follows that a chainreaction can occur, in which each atom which splitscan set off more.

In a critical mass of “ fissile” atoms, if every fissionsets off (say) 2 more, then the chain reaction growsexponentially within a fraction of a second. This isuncontrolled fission, and results in a nuclear explosion of devastating power... an “ atomic bomb” .

If a neutron-absorbing material (such as cadmium) ispresent, it is possible to absorb many of the neutronsso that each fission sets off exactly one other. This iscontrolled fission and is what Fermi achieved in his“pile” in 1942, and what occurs in every nuclear power station.

There are only 2 nuclei which will readily undergofission:


®



13

27

Al2

4

He15

30

P0

1

n+ +

9

19

F0

1

n9

20

F+

Fluorine

Uranium

Bariumisotope

Kryptonisotope

Neutron

Neutron

New, previously unknownradioisotope of Fluorine

92

235

U0

0

1

1

n 3 n

36

92

Kr

56

141

Ba

+

3 extraneutronsreleased.

These canset off otheratoms in a“chainreaction”

92

235

U94

239

Pu

Uranium-235 whichoccurs naturally in

uranium ores, but invery small amounts.

Plutonium-239 which canbe made from U-238 byneutron bombardment ina nuclear reactor.

If the amount of “fissile” atoms is below a certain “critical mass”,most neutrons escape without striking another nucleus, and the

chain reaction is not self-sustaining and dies down.

Start


16/32




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16

Mass Defect During Nuclear FissionThe enormous energy released by nuclear fission is due to a “ mass defect”

between the starting nuc leus and the product nuclei.

For example, in the fission of Uranium-235:

(Note: fission products can vary)

U-235mass

235.0439 u

neutronmass

1.0087 u

La-148mass

147.8114 u

Br-85mass

84.8917 u

3 neutronsmass

3.0261 u

Total Mass beforeFission

236.0526 u

Total Mass afterFission

235.7292

Mass Defect = (Mass Reactants - Mass Products)

= 236.0526 - 235.7292 = 0.3234 u

Energy yield per fission :

Remember that 1 u 931.5 MeVof mass of energy

So, energy released = 0.3234 x 931.5

= 301.2 MeV

(This equates to about 5 x 10-11

joules of energy)

The energy releasedmight seem a very

small amount, but thisis from just one atom.

In (say) 10kg of uranium there are

about 2.5x1025

atoms.If all of these were toundergo fission, the

total energy releasedwould be about 1x10

15

joules, all releasedin a split second, in the case of an atom bomb.

This is the amount of energy generated by anaverage size power station in about 30 years.

Photo byDaron Cooke

Simulated

Nuclear

Explosion

92

235

U0

0

1

1

n 3 n35

85

Br57

148

La+ ++

Practical Work

Observing Nuclear RadiationsYou may have done practical work with one or more

methods of detecting and observing radiation from aradioactive isotope.

The Wilson Cloud Chamber is a simple device which allows the “trails” of alphaparticles to be seen.

The chamber is cooled with “dry ice” so that thevapours within are on the point of condensation.

If a source of alpha particles is placed inside thechamber, tiny “ tracks” can be seen. An alpha particlecollides with air molecules and ionises millions of them along its path. The ionised molecules serve assites of condensation, so a visible “condensation

trail” briefly shows the path of each alpha particle.

Simple SchoolCloud Chamber

Small chip of radioactivematerial

The tracks of

alpha particlesappear as thin“condensationtrails”

This is the plutoniumfission bomb,

nicknamed “Fat Boy”,which destroyed the city

of Nagasaki in 1945.

Enrico Fermiin 1943

working onthe

“Manhattan

Project”

When you add up the totalmass of all the products of a

fission reaction, it is lessthan the starting mass.

This “mass defect” has beenconverted to energy.

E = mc

2


17/32

A “ nucleon” refers to all the particlesa)......................................., and includesb)........................ & ..................................These are different in their properties inthat c).......................... are slightlyheavier, and d)........................... carrye)................ electr ic charge.

The existence of the neutron had beensuspected, and was finally proven byf)...................................... in 1932. Wheng)...............-particles were smashed intoa beryllium target a penetratingradiation was produced. Others had

thought it was h)........................ rays.Chadwick allowed this radiation tostrike a second target of i).......................... This dislodged j)............................ which he could detectand measure their energy. By applyingthe principles of k)............................................................... he could calculatethe properties of the “ mysteryradiation” . His results indicated al).............................. with mass similar to

m).................... but without n)..................................................

“Transmutation” refers to an atomo)..................................................... whenit undergoes a p)...............................reaction. This can occur duringq)....................................... decay, or during nuclear r).......................... or ............................. (opposi te processes).

Alpha decay occurs in a nucleus whichis unstable because s).................................................... It ejects an alphaparticle (which is made up of t)......................................................) so that the MassNumber u)...................................... andthe Atomic Number v)............................................ There is usually emissionof w)............................. as well.

Beta decay occurs when a neutronconverts to a x)............................... Any).......................... is created as well, andit is ejected from the nucleus at high

speed... the beta particle. The AtomicNumber z)..........................................while the Mass Number aa)................................ ..................

It was discovered that the beta particlesfrom different isotopes carriedab).................................... .......................Pauli suggested this was becauseac)...........................................................

which shared the energy with theelectron. This particle is an ad)...........................................

The nucleus is held together by the“ ae)................................................” whichhas to be much more powerful than theaf)....................................... betweenprotons. It acts only over ag)........................ distances, andattracts all ah)......................... to each

other. The force arises from the “ Massai).........................” of the nucleus. Asmall amount of the mass has beenaj)........................ ................... accordingto ak).................................(equation)

Nuclear al).......................... occurs whena nucleus is struck by aam)............................., and thenan).................. ................. It also releases2 or 3 more ao)................................ which

can cause a ap)............................Reaction to occur. During each fissionthere is a large energy release due toaq).............................................................

The first control led fission reaction wasachieved in 1942 as part the secret“ ar).................................... Project” . Thereactor was designed byas)..................................................

17




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Worksheet 5 Into the NucleusFill in the blank spaces Student Name..........................................


18/32




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Alpha Decay EquationsWork out the missing nuclide, identifying

• Mass Number & Atomic Number • Symbol & name

6. Write the equation for the alpha decay of Actinium-227

7. Write the equation for the alpha decay of Plutonium-244

18

86

222

Rn2

+He γ

95

241

Am2

+He γ

84

210

Po2

+He γ

91

233

Pa2

+He γ

84

210

Po2

+He γ

4.

3.

2.

5.

1.

Worksheet 6 Practice ProblemsNuclear Reactions Student Name..........................................

Beta Decay Equations1. If each of the following nuclides underwentbeta decay, write the symbol, Mass Number & Atomic Number of the new nucl ide.

a) Iodine-131

b) Thorium-234

c) Hydrogen-3

d) Sodium-24

e) Uranium-239

f) Cobalt-60

2. Write complete decay equations for the betadecay of:a) Lithium-8

b) Xenon-135

c) Phosphorus-31

d) Chlorine-38

ABN 54 406 994 557

PO Box 2575PORT MACQUARIE NSW 2444

(02) 6583 4333 FAX (02) 6583 9467

www.keepitsimplescience.com.au

[email protected]


Need to contact us?

®


19/32


19


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Worksheet 7 Practice ProblemsMass Defect Student Name..........................................

Data for Calculations

Nuclide Nuclear Mass Nuclide Nuclear Mass

1.0087 1.0073

4.0026 7.0160

24.9575

140.8167

91.8776

21.9780

91.8804

144.8115

235.0439 239.0446

11.99679.01226

12

C

2

4

He

4

9

Be

0

1 n

92

235

U

36

92

Kr

56

141

Ba

3

7

Li

1

1 H

94

239

Pu

38

92

Sr

56

145

Ba

12

25

Mg11

22

Na

(u) (u)

6

12

C2

4

He

3

7

Li

4

9

Be0

1

n+ +

12

25

Mg2

4

He11

22

Na 1

1

H+ +

4.

5.3.

2.

1.

2

4

He2

4

He1

1

H+ +

92

235

U0

0

1

1

n 3 n36

92

Kr56

141

Ba+ ++

94

239

Pu0

0

1

1n 3 n38

92

Sr56

145

Ba+ ++

Use the data table at right.

For each of the following nuclear reactions

calculate:

a) the Mass Defect (u)

b) the energy released (MeV)


20/32


4.Discuss why the neutrino was“ invented” (and by whom) and itsexistence accepted, many years beforeit was physically detected and proven to

exist.

5.a) Explain why a “ chain reaction” of fissions is possible.

b) Compare the requirements for controlled and uncontrolled nuclear fission.

20


®



1.Outline Chadwick’s experiment toconfirm the existence of the neutron,and discuss the importance of “conservation laws” in determining the

neutron’s mass.

2. Account for the need for the “ strongnuclear force” and outline itsproperties.

3.a) What is meant by the “mass defect”of the nucleus?

b) Explain the connections between thestrong nuclear force, the mass defect,and Einstein’s equivalence of mass &energy.


21/32



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Significance of theManhattan Project

Fermi’s first controlled fission chain reaction in 1942was just the first step in one of the most significantscientific research projects in human history.

Within 3 years, fission bombs were used to destroythe Japanese cities of Hiroshima and Nagasaki andbring a sudden end to World War II.

The Manhattan Project brought the world into the“ Atomic Age”, with the following sign ificant changes:

Technologies Developed• Nuclear power stations , current ly meet about 20%of the world’s energy needs. Fission power is“Greenhouse friendly”, but presents the danger of devastating accidents such as at Chernobyl (Ukraine)in 1986. There are also great challenges in the safestorage and disposal of radioactive wastes from

fission power stations.

• Nuclear weapons proliferated during the 40 year “ Cold War” . On several occasions the world seemedto be on the brink of a nuclear war which potentiallycould have destroyed all human civilization.

• Rockets were developed to deliver the nuclear weapons, but the “spin-off” was their use for spaceexploration and satellite technology. The modernworld relies heavily on satellites for communication,commerce and finance as well as entertainment.

• Nuclear Medicine includes all the ways that nuclear technology is used for diagnosis and treatment of awide range of health problems, including cancer.

• Even the humble smoke alarm in your home isconnected to nuclear technology. It contains a tinypellet of radioactive material (Am-241) manufacturedin a nuclear reactor.

Later in this section are more examples, and specificdetails, of technologies which are based on Nuclear Physics and are therefore a direct result of theManhattan Project.

Nuclear Technologies have been widely consideredas having more risks and dangers than benefits.However, there have also been many “ spin-offs”which have been highl y beneficial to society.

Whatever your opinion, the Manhattan Project wascertainly one of the most significant scientificresearch events in human history.

As always, the Science (and the technology it leadsto) is neither good nor bad; that is determined by thechoices and decisions made by people.

21

4. APPLICATIONS OF NUCLEAR PHYSICS

This ruinedbuilding inHoroshima,

Japan, has beenpreserved as a

memorial to themany thousands

who died in theatom bomb

attacks in 1945

Nuclear Physics is Still Investigating Matter

The Manhattan Project, and the “ Nuclear Age”all grew from research by scientists likeChadwick and Fermi who wanted to find outabout the structure of atoms. They used alpha

particles and neutrons as “bu llets” to probe thenucleus to try to understand the fundamentalstructure of matter.

Well, guess what? Scientists are still doing exactly

that, and still using (essentially) the same technique.

Neutrons as Nuclear ProbesNeutrons are still used as probes because their lack of electric charge allows them to penetratethe nucleus more easily than a proton or alphaparticle. A beam of neutrons might be scatteredby a nucleus, or other particles may be ejectedfrom it. This allows scientists to study the

structure of the nucleus.

Particle Acceleratorsare another tool of modern research.

A Part ic le Accelerator uses powerful electromagnets

to accelerate electrically charged particles throughhuge circular tubes. Other electromagnets “ steer”and focus the beam of accelerating particles. At thedesired energy level, the particles are allowed tocollide head-on, or smash into their target. An array of detection equipment studies the particle tracks andradiation from the collision.

For example, the accelerator at C.E.R.N.(underground on the French/Swiss border) is 27 km incircumference, and accelerates particles to velocitiesof 99.995% of the speed of light.

At the end of the section is a brief summary of our understanding of matter, as revealed by the “ atom

smashers”.

Photo ofHoroshima a

few days afterthe bomb.

Parts of the cityliterally “ceased

to exist”.


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22

Nuclear Fission ReactorsThe main peaceful use of nuclear fission technology is to operate controlled chain

reactions in a fission reactor, and use the energy released to make electricity.

There are many different designs. The following schematic diagram

shows the main features of all f ission power stations

Condenser

These areusuallyhuge

coolingtowers

Steam drivenTurbine

&Generator

Electricity

Control Rods are made ofcadmium or boron which absorbs neutrons.Lowering them into the pile slows the chain

reaction; raising them speeds it up.In an emergency, they can be dropped under

gravity to shut the reactor down.

HeatExchanger

Heat fromreactorboils

water tosteam

Fuel RodsUranium or Plutonium

Each rod is less thanthe critical mass,but together they form

well over thecritical mass

needed to sustaina chain reaction.

Each rod can bewithdrawn for

re-fuelling

Heat absorbing fluid (Often a liquid metal)Circulates through the pile and transfers heat tothe heat exchanger for steam production.

Moderator

(usually graphite or “heavy water”)

The reactor “pile” is made of amoderator substance which slowsdown the neutrons. This increasesthe likelihood of each neutroncausing a fission in the nextnucleus it hits.(fast neutrons tend to pass through

without causing a fission)

Photo byLes Powell

The reactor “pile” is inside thisdome, heavily shielded to prevent

any radiation escaping

Sizewell Nuclear Power Station, England

The following is background information only...

Australia is a non-nuclear country.We have one small fission reactor in Sydney for research, and to p roduce radio-isotopes for medicineand industry.

Ironically, Australia is also the country with thelargest mineral deposits of uranium ores. Our economy benefits greatly by selling uranium to other nations, but our government policy (based on the

democratic will of the people) has always been NOTto use nuclear power.

Instead, we rely on hydro-electricity and on burningfossil fuels. Most of our electricity is made by burningcoal, which is a major contributor to the “GreenhouseEffect” and Global Warming.

Many people believe that nuclear technologies havebeen improved, and are now safe enough for Australiato look towards nuclear power for our growingenergy demands.

Please have an opinion on this important issue,

but make sure it is an informed opinion.


23/32

23

Uses of Radio-isotopesin Medicine

One application of Nuclear Physics that is likely toaffect each of us, or our family, is the use of radio-isotopes in health care.

Radio-isotopes are used for:

Imaging and DiagnosisRadio-isotopes have now joined X-rays andultrasound scans for medical imaging and diagnosis.

For example, the artificial isotope thallium-201 isused with a “ gamma ray camera” to image heartmuscle and detect any damage from heart disease.

When injected into the bloodstream, thallium tends tocollect in any active muscle because it “mimics”potassium ions. Being radioactive (it gives off a lot of low-energy gamma rays) it allows a gamma raycamera to make computer-aided images of heartmuscle to identify if any part of it is damaged.

The isotope has an extremely short half-life, so itrapidly disappears and presents little danger to thepatient.

Cancer Treatment“Radiation therapy” relies on the fact that rapidly-dividing cancer cells are more easily killed by gammaradiation than normal healthy cells.

The isotope cobalt-60 (which emits beta and stronggamma radiation) is commonly used as a source of radiation which is accurately beamed into the tumour.

Radio-isotopes in IndustryThe gamma rays from cobalt-60 are verypenetrating, and very destructive to living cells.

In the manufacture of medical supplies, such asbandages and dressings, it is vital that theproduct is totally sterile (germ-free). This isachieved by irradiating the products with dosesof gamma radiation high enough to destroy anybacteria or fungi spores which might be present.

In paper manufacture, alpha emitting isotopessuch as Americium-241, are used for thicknesscontrol. A radiation detector constantlymeasures the percentage of radiation whichpenetrates the paper as it moves at high speedthrough “ thicknessing” rollers. If the radiationlevel drops, this means the paper is too thick, sothe rollers are automatically adjusted.

Radio-isotopes in EngineeringIn aircraft construction, the airplane parts maybe welded together. It is essential that thewelded joints are totally strong and free of defects. X-rays are not able to penetrate themetal welds, but gamma rays can.

To “ see” inside the weld, gamma rays (again,cobalt -60) are used like X-rays; they are beamedthrough the welded joint and an image capturedby a “ gamma-ray camera” . Analysis of theimage allows engineers to be sure of the qualityof the welding.

Radio-isotopes in AgricultureRadio-iosotopes are not used directly infarming, but are very important in Agricultural

research, such as that carried out by the CSIRO.

For example, to study and compare the rates of uptake of fertilisers into crop plants, isotopessuch as nitrogen-15 and phosphorus-32 arecommonly used.

Small concentrations of these isotopes can beincluded in a fertiliser applied to experimentalplants. The uptake of the fertiliser, and where itends up in the plant, can be “ traced” by usingradiation detection equipment. This researchultimately helps farmers to produce food cropsmore efficiently and economically.


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Another example is the use of iodine-131 in the

treatment of thyroid cancer. The thyroid gland islocated in the throat, and produces a vitalhormone which has iodine atoms in it.

This gland is the only part of the body whichuses iodine, and enzymes in the gland are ableto chemically “ recognize” iodine ions and veryefficiently “ harvest” iodine from the bloodstream.

Iodine-131 is radioactive and emits beta andgamma rays.

If a small amount of I-131 isinjected into a patient who hasa tumour in the thyroid gland,the radiation level is so low

that there is little risk to their healthy tissue.

However, due to the chemistryof the iodine, the thyroidgland rapidly absorbs the

isotope and concentrates it.The radiation is concentratedin the “ target organ” and isvery effective in destroying

the tumour.

I-131 has a short half-life and

the radiation disappearsrapidly.

Location of ThyroidGland


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The “ Standard Model” of Matter After 100 years o f scient if ic research in to the sub-atomic quantum universe,

just what i s the latest “ picture” we have for the st ructure of matter?

Our modern understanding is known as the “ Standard Model” ,

and is a description of both matter and energy (since these are inter-changeable)

at its most fundamental l evel.

The Four Fundamental Forces:

Gravity (the weakest of all) acts between all masses, and holds planets,stars & galaxies together and in orbit.

Electomagnetic Force acts only between charged particles. It isresponsible for holding atoms and molecules together (all chemical bondsare basically electrical) as well as causing all electrical and magneticphenomena.

The Nuclear Weak Force is involved in radioactivitysuch as when an electron and an anti-neutrino are producedduring beta decay in the nucleus.

The Nuclear Strong Force (the strongest of all) actsonly between particles of the “ hadron” family. It acts only over very short range and is what holds protons and neutronstogether in the atomic nucleus.

We now know that protons & neutrons are composed of smaller particles called quarks.

The Structure of Matter Many Particles, but Just Two Families.

Once the “atom-smashing” Particle Accelerators were developed, scientistsbegan detecting a bewildering assortment

of sub-atomic particles.

This confusion has now been simpli fiedwith the realisation that all these particles

belong to just 2 basic types or classes:

Leptons & Hadrons

Leptons

include the electron, and theneutrino family.(there are several

types of neutrino)

As well as being the particleswhich flow in an electriccurrent, electrons are athome in orbit around a

nucleus. Remember too, thatthey have wave properties

and form (de Broglie’s)“standing waves” within(Bohr’s) allowed orbits.

When formed in the nucleusduring beta decay, the

electron (and an anti-neutrino) is instantly ejected

at high speed.

Then there are the

BosonsThese are quantum “ particle-waves” and are the means by

which all t he particlesexert forces on each other.

The best known is the “photon”of electromagnetic radiation,

such as light.

Gravity is thought to involve“gravitons”, but these have notyet been proven to exist.

The nuclear forces are carriedby gluons (strong force) and

W-particles (weak).

Hadrons are made from QUARKSHadrons include the proton and neutron, and a family of particles called mesons.

Al l the hadrons are composed ofcombinations of “ quarks” .

Each quark has a charge of either +2/3 or -1/3(compared to the charge of an electron = -1).

Protons contain 3 quarks with charge = +2/3 +2/3 -1/3 = +1Neutrons contain 3 quarks with charge= +2/3 -1/3 -1/3 = 0

Quarks themselves come in a variety of “flavours” whichhave been given whimsical names such as “charm” and“ strange”. These names are labels for quantum states andbear no connection to the normal meanings of these words.

Anti-Partic les and Anti-Matter It has been discovered that for every Hadron and Lepton that exists, there is also a corresponding anti-particle.For example, there are electrons , and there are anti-electrons (“posi trons” ) which have the same mass, butopposite electric charge. There are also anti-protons, anti-neutrons, and so on. As you know, the other particleformed in beta-decay is an anti-neutrino.Theoretically, there could exist “ anti-matter” with atoms made entirely of anti-particles.

When any particle and its anti-particle meet, they mutually annihi late each other... all the mass is converted intoenergy (photons of gamma radiation) according to E=mc

2.

So far, it has NOT been possible tocombine Quantum Mechanics and the

Standard Model of Matter withEinstein’s Relativity Physics.

This would be the GUT; “Grand UnitedTheory”, which would combine an

explanation of EVERYTHING.


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Worksheet 9 Applications of Nuclear PhysicsFill in the blank spaces Student Name..........................................

The Manhattan Project brought theworld into the a).......................... Age andwas one of the b)...............................scientific research projects in history. It

led to technologies such asc)......................................... from whichthe world gets about 20% of itselectricity. d).......................................were a threat to civilization during the“ e)............................ War” . Rockets weredeveloped to carry weapons, but nowwe rely on them for f)......................................................... The many uses of g)............................ substances inMedicine and Industry are also direct“spin-offs”.

Nuclear research is still going on.Neutrons are excellent “ probes” or “ bul lets” because h)................................................... In addition, i)........................................................ are used toaccelerate j)............................... particlesup to near the k).............................................. From the l)....................& .................... from a collision,scientists are able to infer the structure

of matter.

A nuclear fiss ion reactor has 3 maincomponents:• Fuel Rods made of a “ fissile” materialsuch as m)................................. or ...................................• n)........................ Rods (made of o).......................) These control the rateof fission by absorbing p).........................• The Moderator, which is usuallyq)................................. or “ heavy water” .Its job is to r).................................... theneutrons so that fission is more likely tooccur. The energy released by thefission reaction is used to make steam,which then drives a s).............................and ............................. to maket)...........................

Nuclear reactors not only provideelectricity, but are used to make manyartificial u)............................... isotopesthat are useful in Medicine and Industry.

Medical uses include v).............................and diagnosis, as well as treatingw)..................... by irradiation. An isotopeused for imaging is x).............................,while y)........................ radiation for cancer therapy often comes from theisotope z).............................

This same isotope is also used inindustry, for example, to

aa)...................................... surgicaldressing and bandages after manufacture and packaging. In paper manufacture, the isotope ab)....................is used to control the thickness bymeasuring the penetration of ac).............................. through the paper.

In engineering, gamma rays fromad)......................... are used to check thequality of ae)..........................................,for example in aircraft construction.

In agricultural research, isotopes suchas af)...................... and .............................are used to “ trace” the movement of chemicals into and through a plant.

Our modern “ picture” of matter is calledthe ag)................... ..............................There are many sub-atomic particles,but they all belong to 2 classes:• ah)........................, including the

electron and a variety of ai)......................• aj)..........................., including theak)....................... and ............................Each of these is composed of smaller (although more massive) particlescalled al)...........................


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CONCEPT DIAGRAM (“ Mind Map” ) OF TOPICIn all the Core Topics you were given examples of a “Mind Map”

as a way to summarise the content of the topic.If you have found this a useful way to summarise and learn, then you may want to do it again.

By now you should have developed the skills to do it yourself...

Into theNucleus

FROM QUANTATO QUARKS

Rutherford & Bohr

Models of the Atomde Broglie

&Matter Waves

Applicationsof

Nuclear Physics


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Answer Section

Worksheet 11.

2.The existing theory for EMR stated that electronsaccelerating in circular motion should constantly emitlight energy, but obviously they don’t.

3.a) Balmer Series is the 4 lines of visible light in theemission spectrum for hydrogen.b) 1 = RH( 1/nf

2- 1/n i

2)

λ

= 1.097x107( 1/2

2- 1/4

2)

1/λ = 2.057 x 106

∴ λ = 4.86x10-7 mc) c = λ .f, ∴ f = c/λ

= 3.00x108

/4.86 x10-7

= 6.17x1014

Hz.E = h.f

= 6.63x10-34

x 6.17x1014

= 4.09x10-19

J.d) The energy difference between the 2nd and 4thquantum levels (or “allowed orbits”).

4.It is very unlikely that Bohr could have developed hisatomic model without the evidence of the hydrogen

spectrum. The fact that there were distinct lines atprecise wavelengths all pointed to quanta of energy,rather than variable amounts.

5.a) More energy, because it is the difference between5th-2nd orbits, compared to 4th-2nd.b) Higher frequency, because Plank’s E = hf shows adirect relationship between energy and frequency.c)Shorter, because frequency and wavelength areinversely related by the wave equation , v=lf.

6.a)• electrons revolve only in certain stable, “allowedorbits”• Energy must be absorbed, or emitted, in quantisedamounts when an electron jumps from one

photomaster - phys8 - from quanta to quarks

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