nuclear physics copy

8/10/2019 Nuclear Physics Copy

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Nuclear Physics:

Artificial transmutationthe change of one element to another through the bombardment of a nucleu(Rutherford).

Rutherford determined through cloud chamber experiment that the alpha particle was absorbed whencollided with a nitrogen nucleus:

decay, the weak interaction converts a neutron proton while emitting an electron (e-) and an anti-neutr

+ decay, energy is used to convert a proton neutron, a positron (e+) and a neutrino.

ome nuclei have a larger neutron-proton ratio and thus a relatively larger strong nuclear force as opposed to itsepelling electromagnetic force. Those nuclei are more stable.

h7 Atomic and Nuclear Physics

Thomson model: the plum pudding model. Positive pudding with negative plums (electrons).

Rutherford model: like a mini solar system. The flaw was that the electrons would radiate electromagnwaves, lose energy and spiral into the nucleus.

tomic spectra: give atoms energy and they produce light as the electrons travel up the shells. Split up the ligh

nd the different wavelengths. Electrons only have certain amounts of energy in the first place (quantized). Th

hown by the atomic spectrum as it only releases certain amounts of energy (the thin lines). This means that o

ertain energies are possible for different elements (proves energy levels) discrete.

his means light must be quantized, as it is not a continuous wave.

mission spectrum: a spectrum of light emitted by an element; a series of bright lines, with dark gaps betwe

he lines where no light is emitted.bsorption spectrum: a bright continuous spectrum covering the full range of visible colors, with dark lines

where the element absorbs light.

When an electron falls between two energy levels it will emit a photon equal in energy to the differencenergy levels. The energy of a photon is dependent on its frequency. Thus, the existence of discrete

wavelengths in the spectrum is evidence that energy levels are discrete.

.2 Quantum Nature of Light


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Photoelectric effect: electrons are only emitted if the light source is very bright. If it is dim, we expect n

electrons to be emitted. If some are, there is a time delay as they collect energy. Lower frequency light w

work if still bright enough.

Zinc plate experiment: a zinc plate on an electroscope with UV light shining on it. Lost electrons meanscharge, so electroscope leaf should fall during the photoelectric effect. But: when dim, there was no tim

delay, but fell slower. Lower frequency (despite intensity) did not emit any electrons.

Quantum light model: made up of packets of energy called photons. E = hf for photon. UV has a high frequency, so it gives enough energy to the zinc plate to emit electrons. Lower intensity

means less photons, means less rapid electron loss (but no delay). Low frequency means low energy

photons, means it cannot free electrons.

Millikan created an experiment to find the KE of electrons. He created and electric field and increases tenergy until no electrons could pass through. He used this stopping potential to find the fastest KE:

E loss = PE gain

/2mv2

= VSe

EMAX = VSe

igher intensity = higher current, same potential. (More plates but the same energy amount VS).

hreshold frequency: the frequency at which photoelectrons are liberated. Max photoelectron KE = energy of

hoton energy needed for release KEMAX = hf ( = work function.)OR KEMAX = hf hf0

or photon frequency, change in energy E = hf (for energy levels).

bsorption spectrum: has white lines in the rainbow where electron has absorbed the frequency needed for th

o escape. Proves electron energy levels.

.3 Wave Nature of Light


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lectron gun: filament is made hot by AC current. Electrons are liberated. They accelerate towards anode by

ccelerating p.d. Pass through with constant velocity:

= (2/)1/2

hosphorescence: electrons when going down energy level(s) emit light.

e Broglie Hypothesis: all matter has a wave-like nature. = h/

or example, electrons passed through a thin film of graphite create a diffraction pattern (wave-like property)

robability waves: diffraction maps out all the possible results.

Davidson-Germer experiment: a beam of electrons reflected off a nickel crystal. Angle of max intensity be explained in terms of constructive interference between De Broglie waves reflected off layers of ato

(supports De Broglie hypothesis).

Heisenberg uncertainty principle: we cannot know momentum and positive accurately. We can either: through a small slit (know definite location, but it will be diffracted momentum?) or pass through a la

slit (definite momentum, will not deflect, so no definite location).

or momentum and displacement: x > h/4

or energy and time: E t > h/4

.4 Quantum Atom Models

Electron in a box: an electron isnt free to move outside the atom. To model this, think of a string clamp

at both ends. It can only have certain frequencies (the harmonics), like an electron can only have certai

energies. To create a quantum model, think of it as a probability wave trapped in a box.

Schrodingers Model: he realised the electrons position probability was not as simple as the sine wave previously. The wave function is called Schrdingers equation () and the probability of finding the

electron is 2

. His model predicted the most likely electron position. It showed that some energy

transitions are more likely, and why some spectral lines are brighter.OR HYDROGEN:


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.5 Nuclear Structure

Mass of the nucleus: found using mass spectrometer. Projected at right angles to a uniform field; pathradiusmass. m = BQr/v. The ion experiences two forces (magnetic force and electric force) so v = E/B

ounting the number of dots on the photographic plate is the number of ions.

Charged particle scattering experiment: like Geiger-Marsden experiment. Deflected alpha particles hit anucleus. The KE can be calculated, and distance too. To find the nucleus size, they fired faster alphas un

they no longer returned. The faster ones got the closest.

uclear force: very short, short range force holding nucleus together (same for all nucleons).

Binding energy: the amount of work required to pull apart a nucleus. E = mc2

. The energy is converted

mass (not KE, as the nucleus is not moving).The binding energy curve of a nucleus is found by the

difference between the mass of the nucleus and mass of the parts (the mass defect).

arge nuclei are less stable as they have more protons pushing the nucleus apart. All systems will try to reach

west possible energy. BE is released when a nucleus is formed, so changing to higher BE means energy is

eleased (so higher BE = good/more stable).


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uclear mass is measured in (u). 1u = 931.5MeV. BE = mass defect.

E per nucleon = mass defect/nucleon number.

l on the left of Fe undergo fission as it attains a more stable state with combined mass leading BE.


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Nuclear Physics:

Artificial transmutationthe change of one element to another through the bombardment of a nucleu

(Rutherford).

Rutherford determined through cloud chamber experiment that the alpha particle was absorbed whencollided with a nitrogen nucleus:


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mallest unit of charge possible.

1.4 : This means that charge must be quantized (only come in discrete bits, not continuous), and the quantuharge was 1.6 x 10-19C.

1.5 : An electron gun relies on the principle of thermonic emission. There is a large PD created between twoetal plates in a vacuum. The cathode (the one from which the electrons come) has a hole in it, and so some o

he electrons fly through and create a sort of beam of electrons (originally called a cathode ray)

or what it's worth,Miten Shahoffers this advice about remembering that the cathode is negative, and the anoositive...

Well I remember it like this, maybe it will help some of you confused souls...hehe

cathode - negatve ......."C" anode - posivte ......... "A+"

1.6 : Cathode rays can be deflected by both electric and magnetic fields, and act as negatively charged particould in such fields. both these properties can be explained by the fact that they are actually electrons.

1.7 : Thompson's experiment involved using electric and magnetic fields to exactly cancel each other's effectnd allow an electron to pass undeflected. The electric field is then removed and the radius of curvature is theneasured. The equations then simplify down to give an expression for e/min which all the other terms are know

nd so the ration could be accurately found.

1.8 : By knowing the charge of an electron (Millikan) and the charge to mass ratio (Thompson) it is possible

nd the mass of an electron...So that makes Thompson the discoverer of the electron...well horray for him.

1.9 : The alpha particle scattering experiment involved firing alpha particles at a sheet of very thin gold foil,

etecting where they went (with a screen).

1.10 : The results of the above experiment were that the majority of alpha particles passes straight through.

hose which were deflected, many were deflected through very large angles, and even straight back at the souhis result suggested that atoms consisted mostly of empty space, whit a small nucleus of high positive charge

1.11 : Rutherford's model was therefor that around the small, highly charged nucleus, electrons orbited like

anets around the sun. This created many more questions...why didn't the electrons emit radiation and lose

nergy...and how would they be kept in a constant orbit.

.2 Nuclei and their constituents

2.1 : Radioactive decay is basically atoms (or more specifically nuclei) spontaneously breaking off small parts

alpha, beta and gamma particles) of themselves. This was accidentally discovered due to the effects of thesearticles on photographic film which was being kept in a drawer with them. This lead to a systematic analysis o

uch particles, and the elements which produced them. The three different types mentioned above were found

eparated, and the effect on the atoms undergoing this process (changing elements from one type to another) xamined.

2.2 : The three types of radiation were first divided by their ionising power. Rutherford later showed an alpha

article to be the nucleus of a helium atom by measuring their emission spectra. Beta particles were found to bee electrons, but emitted from the nucleus as a result of the changes which occurred in it. Gamma rays were

und to be a type of very high frequency electromagnetic radiation.

2.3 : The products of alpha and beta decay are quite easy to find...simply write out and balance the nuclearquations...

X -> A-4Z-2Y +42He ... then determine what element and isotope Y is.

2.4 : Radiation tends to ionise (strip the electrons from) gases when it passes through. This fact is used the tetection of radiation with geiger counters. (no real detail is required here)

2.5 : AZX -- A is the mass number, the number of nucleons or whatever else you'd like to call it...the number rotons + the number of neutrons. Z is the proton number, the atomic number...the number of protons. To finhe number of neutrons, obviously, subtract Z from A.

2.6 : Artificial transmutation ... cool name for a somewhat boring thing ... when atoms decay, they change in

fferent atoms, and this is called artificial transmutation. Atoms usually only lose alpha and beta particles (gamjust a loss of energy, so not relevant here). An alpha particle is 2 protons and 2 neutrons. A beta particle is 1
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egative charge, effectively a neutron turning into a proton in the nucleus. These facts can be put together to

redict the results of nuclear equations.

2.7 : Describe how the reaction between N and He led to the discovery of the proton...By bombarding nitrogeuclei with alpha particles, Rutherford caused the ejection of hydrogen nuclei and the production of a new oxyg

ucleus. As a result, the proton was discovered.

2.8 : The proton is the thing in the nucleus of a hydrogen atom, and there are an increasing number in other

tom's nuclei. It has the same magnitude of charge as an electron, though of positive rather than negative.

2.9 : Radioactive decay is a random process for individual atoms, but overall, a block of radioactive atom's ra

f decay is exponential, falling to zero eventually. The decay rate can not be affected by physical or chemicalonditions. For a large number of atoms, the number of radioactive atoms will halve over a regular period of timalled the half life, and this results in the exponential nature.

2.10 : Half life is the period of time (average, though accurate for a large number of atoms) required for the f decay of a radioactive sample to decrease to half it's initial value. This is a constant for a given isotope.

2.11 : The half life life can be determined from a graph by taking a point on the graph, finding it's rate, findinhe rate which is half of this, then finding the point on the graph which corresponds to this half rate. The half lihe time, as it is on the x-axis, between the two points.

2.12 : The reactivity after n half lives will be Initial x (1/2)n. (not in data book, but fairly obvious...)

3.1 Atoms and their constituents

3.1.1 : Millikan's oil drop experiment involved first producing small droplets of oil with an atomizer. Some ofhese then fell through a small hole, and into a region between two fields. Using a variable resistance, the

rength of the field was adjusted until the upward force of the field (The +ve plate was up the top, -ve on theottom, but could be reversed for drops of opposite charge) equals the downward force of gravity. after it was

alanced, the voltage was recorded, and then the drop was allowed to fall. After falling some distance, therop falls at a constant speed (where the force of gravity is equaled by the air resistance). This terminal speed

measured, and allows the mass to be found using Stoke's law.

hen, we equate Fgand Ff, as follows ... qE = mg ... q =mg/E. Since the mass of the drop can be found, and

oth g and E are known, we can find the charge of the drop. By graphing these charge values, we find that themallest difference between them is e, 1.6 x 10 -19C.

3.1.2 : Thompson's experiment is based around the counteracting effects of electric and magnetic fields.rst, the two fields are adjusted so the beam passes undeflected between them, with the deflection effects of

ach equaling out ... Therefore, Fe= Fb, and so Eq = Bqv therefore v =E/B. The electric field is then removed,

eaning the beam is deflected downwards by the magnetic field. Since the force from a magnetic field = evB,om Fc= mv

2/ r we get evB = mv2/ r. this simplifies down to e/m=v/Br. We can measure the radius of

urvature, we know the velocity from above, and we know the strength of the B field, and so the value of

mcan be found.

3.1.3 : The distance of closest approach of a particle to the nucleus can be found by the conservation of

nergy. The initial energy of the particle is defined by Ek=1/2mv

2. This energy is converted into potential

nergy as the charge approaches the nucleus. The potential energy at a given point is equal to the work doneo move the charge to that point, so W = qalphaV. V for a radial field is 1/ (4 x Pi x Eo) x qnucleus/d, so theotential energy is (qalphaqnucleus) / (4 x Pi x Eox d). When this is equated with the kinetic energy, all the terms

re known except the distance, which can therefore be found.

3.2 Nuclei and their constituents

3.2.1 : The mass spectrometer ... First we start with a source of ions, all with a +1 charge. These areccelerated through an electric field. These ions then enter a velocity selector, an area with both magnetic and

ectric fields applying a force in opposite directions, so as to cancel each other out. This, as above the two

rces equal out, and we get Fe= Fb, and so Eq = Bqv therefore v =E/B. Thus, only ions with a particular speed

re allowed through to the next stage. The electric field ends, and the ions are deflected through a magneticeld, resulting in a circular path. This means there is a centripetal force supplied by the field, and so mv2/ r =

qv, which rearranges to m = Bqr/v. Assuming the B field is varied to keep the radius constant, mass isroportional to magnetic field strength, as everything else is constant.

3.2.2 : How Chadwick discovered the neutron, thanks toJonathan Chui.


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hadwick discover the effect by bombardment of Beryllium with alpha particles. A wax block (with its chain of

ydrocarbons it serves as a proton source) is placed after a short distance, and protons are detected after the

ax block. Thus there must be some way to 'knock out' the proton. From the energy the protons are in, theompton effect due to possible gamma ray emission is too low to compensate. If the particle that alphanocked out is a neutron though, it fits perfectly both by the conservation of energy and the conservation of

omentum (since the p and n have approx. same mass, we would expect the 'pool players' result') Yet thesearticles are indeed uncharged. Further more, when these are to collide with protons in cloud chambers, aght angle track would result.

3.2.3 : Beta decay and the neutrino...

he mechanisms are ... p -> n + e+

+ a neutrino (written like a curly v) and n -> p + e-

+ an antineutrinowhich is the same curly v with a bar on top).

3.2.4 : decay chains ... Everything can be written as a series of nuclear equations ... such as AZX +0-1e ->

AZ-

Y, the totals must be kept constant on both sides, but it's fairly easy.

3.2.5 : The equation N = Nox e-lambda x tis in the data book, while delta-N/delta-t= -lambda x N is not. Both can be

sed to find decay stuff. N is the number of radioactive nuclei, Nois the starting number and lambda is defined

s ln2/half life(that's in the data book).delta-N/delta-tis the rate of decay.

3.2.6 : deduce lambda = ln2/half life. We start by taking a time after one half life, therefore N = No/2. Therefore,

= Nox e-lambda x tbecomes 2 = e-lambda x t. We then ln both sides to get ln2 = lambda x t0.5, and this rearranges

o the required expression.

3.2.7 : By coulomb's law, the protons in the nucleus should all repel each other and break it to bits.herefore, there must be another force holding it all together, called the strong nuclear force. This is a forcehich greatly outweighs the electromagnetic repulsion, but only acts over a very small distance (within the

ucleus).

3.3 Energy changes within atoms

3.3.1 : Atomic emission and absorption spectra result from the fact that electrons can move between energyvels when they have sufficient energy put in. They will then fall back, emitting a defined amount of energy

s light. emission spectra result from electrons being excited by electricity or something, then emitting light ashe electrons fall back. Absorption spectra result from electrons absorbing energy from electromagnetic

adiation, and so effectively blocking it. In the emission case, there will be a series of thin bands representing

he wavelengths of light produced, and for absorption, there will be a full spectrum with some lines cut outhe wavelengths that were absorbed).

3.3.2 - 13.3.4 thanks toJonathan Chui3.3.2 : State Bohrs postulates a)Some stable orbits exists (assumed circular) b)electrons absorbs/emitsnergy in changing orbits c)Quantum condition (rules for changing orbit) : mvr = n (h/2*pi), where

=1,2,3,... This formula can be derived by equating Angular momentum L with n * hbar (hbar means

/2*pi). Historically it is based on expt discovery. We'll call it *1 later.

3.3.3 : Describe the spectrum of atomic hydrogen and account for it, using Bohrs' model. (This account

hould be slightly more detailed than that required by the IB.) The charge in the nucleus = Ze charge inectron = e Assuming a circular path, centripetal force = m(v square)/radius. Since this force is supportedy the electronic attraction, m (v square) / r = k (Ze)(e)/ (r square) Simplifying we obtain r = k (Z)(e

quare)/ m(v square). Let's call it *2

rom above *1, mvr = n (hbar), thus rearrangin we obtain v = n (hbar)/mr. Plugging into *2, simplify and

ou'll obtain a equation, which relates the orbital radius with (constant)(n square). Energy of the electron =E + PE = 1/2 m(v square)+ k Z(e square)/r. Substitute v by expression *1, we'll arrive at E at nth shell =constant)/r at nth shell. Since r is proportional to (n square), E = (constant)/ n square. (required byB) Knowing this and E = hc / lambda (Planck's equation), you'll also need to know the Rydberg eqn. This is

hown in the syllabus, and can be easily derived from the above.

3.3.4 : Evaluate the success and limitations of Bohr's model

uccess: 1) Explains why atoms emit and successfullly predict emission for Hydrogen. 2)Explains whytoms absorb 3)Ensures the stability of atoms 4)Predicts accurately the ionisation energy for Hydrogen.

mitations:

1)Not successful for multi-electron atoms.

2)Can't explain fine structures (emission lines


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xisting as 2 or more close lines) 3)Can't explain bonding of atoms in molecules or solids & liquids 4)Can't

xplain different intensity of spectral lines.

3.4 Energy changes within nuclei

3.4.1 : Einstein's mass-energy equivalence ... delta-E = delta-m x c2... yey ... E is in joules, and m inlograms.

3.4.2 : term definitions...

nified mass unit ... one twelfth the mass of a carbon 12 atom ...

ass defect ... the amount of mass which is converted into energy in a nuclear reaction.

nding energy ... the energy equivalent of the difference in mass between the nucleus of an atom, and the

asses of the individual protons and neutrons which make it up.

3.4.3 : The binding energy can be calculated as described above, but finding the total mass defect between

he individual nucleons, and the whole nucleus. The binding energy per nucleon is therefore, this divided byhe number there are.

3.4.4 : The graph of atomic number vs binding energy per nucleon runs from Z=2 increasing rapidly (with apeaks I don't think we need to worry about) to about Z=20 where it runs relatively flat at around 8 Mev perucleon then begins to drop off after Z = 60. The higher an element is (ie the more binding energy it has) the

ore stable it will be, and so the most stable elements are those around Z = 20.

3.4.5 : Fission is the process by which an atom breaks up into smaller fragments. This is often caused by the

ddition of neutrons to the atoms, causing it to become unstable and eventually break up. This breaking up

ay, in some cases, produce more neutrons, and so these can then go on to produce more fission reactions,reating a chain reaction which perpetuates itself.

3.4.6 : Fission is good because it provides a lot of energy form a source that is more viable long term than

ssil fuels, and because it is relatively clean in terms of air pollution compared to fossil fuels. The down side, it produces radioactive material which must be stored somewhere, and also, it can be dangerous if not

ontrolled properly (meltdowns and stuff...)

3.4.7 : Nuclear fusion occurs when two smaller nuclei fuse together to form one bigger, and more stableucleus, and produce lots of energy in the process. Initiation of fusion requires a great deal of heat, because

he nuclei must be given enough initial energy to overcome the coulomb repulsion between them as theypproach. Energy calculations can be done using E = mc2, when the masses of the different fragments are

ven.

3.5 Interaction of matter and energy

3.5.1 : The explanation of the photoelectric effect is that the energy carried by light is broken into discrete

nits, the size of which depend on the frequency of the radiation. the energy carried in each 'photon' is defineds E = hf (plank's constant x frequency). The atoms require a certain amount of energy to release an electron,

Wo= hfo. where Wois called the work function. if there is more energy than this, then that may be given to theectron in the form of kinetic energy, and so E = hf = Wo+

1/2x m x vmax2.

3.5.2 : The photoelectric effect can be measured by applying a stopping voltage in the opposite direction to

he current induced by the photoelectron emission. As the frequency of the light is increased, more energy wille required to stop these electrons. If the frequency is decreased, however, there is eventually a point where

o emissions occur, and so no voltage is required. hf = hfo+ eVs, where Vsis the stopping voltage.

3.5.3 : X-rays are produced by first placing an anode and cathode in a vacuum tube. Behind the anode is

ome type of photo-sensitive material, and between the two is a potential difference of about 150 000v. Theathode is heated to produce thermo-electrons. These electrons the accelerate towards the anode. When theectrons are deflected, by coming close to the nuclei, their kinetic energy changes. This change results in the

roduction of an x-ray. Since the electrons can come as close or as far away from the nucleus, the x-ray

pectrum is continuous, not discrete. There are, however, peaks caused by inner shell electrons being excitedy small energy loss. These peaks occur on the left side of the curve, which is generally an inverted parabolaype shape. There is a shortest wavelength possible for the x-rays due to the fact that when electrons lose all

heir kinetic energy, there is not way to make higher frequency waves.


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3.5.4 : When electrons lose some of their energy, x-rays are produced...the short wavelength limit is when

hey lose all of it so eV = hc/lambda=1/2mv

2. and then lambdamin=hc/eV... there's some other stuff I should

ome back to.

3.5.5 : DeBroglie's equation is ... lambda = h/p. Thus, we can see that all mass has a wave equivalent, and

ny wave has a mass equivalent.

3.5.6 : the velocity of an electron can be found from 1/2mv2= eV, and this can then be used in the equation

v=h/lambda, to find the electron's wavelength. This can be seen/verified by the diffraction of electrons through

hin crystals, showing that electrons have a wave nature.

3.6 Particle physics

3.6.1 : Linear accelerators are designed based on a series of 'tubes' through which the particles are pulled,nd then pushed by electric fields. The lengths of the tubes become longer and longer so the frequency with

hich the electric fields must oscillate are constant.

3.6.2 : Circular particle accelerators work on the basis of magnetic fields making the particles rotate, and

hen they cross between the two Ds, they are accelerated between them by a electric field. The radius insidedefined by r = mv/Bq, and so as the velocity increase, the magnetic field must be increased to keep the radius

onstant.

3.6.3 : When a particle having been accelerated collides with a fixed target, both usually break up intomaller fragments. These can sometimes be identified in a cloud chamber.

3.6.4 : Particle anti-particle pairs are only really produced from interactions involving great amounts ofnergy. Then two such particles collide, the completely annihilate, producing only energy.

3.6.5 : particle / anti particle pairs ...

ectrons - positrons (these are less common, but technically, electrons are the anti particle).

roton - antiproton (these are the same except for charge...same as above)

hoton - photon (same particle)

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