317

Modern Physics

318

Modern Physics

The Dual Nature of Light

Historically, light has sometimes been viewed as a particle rather than a wave; Newton, for example, thought of light this way. The particle view was pretty much discredited with Young's double slit experiment, which made things look as though light had to be a wave. But in the early 20th century, some physicists (Einstein, for one) began to examine the particle view of light again.

What proof exists that light is a wave?

• Diffraction • Interference • Doppler Effect • Polarization

The Photoelectric Effect

Einstein noted that careful experiments involving the photoelectric effect could show whether light consists of particles or waves. Because the details of the photoelectric effect come out differently depending on whether light consists of particles or waves.

Predictions According to Classical Wave Theory Experimental Results

1. The photoelectric effect should occur for light

of any frequency or wavelength.

2. Waves possessing more energy would cause

more electrons to be released.

• Energy = Intensity = Amplitude

1. The photoelectric effect does not occur at all

if the frequency of the light source is below a

certain value (threshold frequency).

2.

• For frequencies above the threshold

frequency, increasing the intensity

increases the number of electrons

• For frequencies below the threshold

frequency, it has no effect.

What proof exists that light is a particle?

• Photoelectric Effect - when light shines on a metal surface, the surface emits electrons.

• Photocell – a device that utilizes the photoelectric effect to create a current.

Particle-Wave Duality – a model which states that light can exhibit properties of both waves and of

particles.

ex – solar panels

DEMO – zinc (newly cleaned w/ steel wool), uv light source, electroscope; place zinc on electroscope, charge electroscope negative, shine uv light on zinc which will discharge scope.

Discovered by Heinrich Hertz in 1887

DEMO – Photocell – connect the ammeter to the photocell, shine a regular light bulb onto the photocell and the ammeter shows the current (hold ammeter up so students not looking directly at light bulb.

In the end they compromised – it is both a wave and a particle

The experimental results suggest the complete failure of

the wave theory to account for the photoelectric effect.

319

Blackbody Radiation

At the turn of the century scientists were puzzled just how heated bodies radiated.

• Scientists Hertz and Maxwell predicted that heat causes molecules and atoms to vibrate. Since atoms are composed of electrical charges, when they oscillate, they emit electromagnetic radiation.

Planck's Constant

• In 1900, Max Planck was working on the problem of how the radiation an object emits is related to its temperature. He came up with a formula that agreed very closely with experimental data, but the formula only made sense if he assume that the energy of a vibrating molecule was quantized - could only take on certain values.

• Based on Planck's work, Einstein proposed that light also delivers its energy in chunks, meaning light consists of little bundles, or quanta, called photons.

o Quantum – the smallest value of any physics quantity.

Photon ( gammaγ = ) – a discrete quantity (or “packet”) of electromagnetic energy that has

momentum, is massless, and travels at the speed of light

Planck discovered that energy of a photon depends on

• Frequency

• Planck’s constant (h) = 6.63 x 10-34 J•s

Energy of a Photon

Photoelectric Effect Equation

• Work function (Φ)– the amount of energy an electron must absorb to be liberated during the

photoelectric effect

• Any excess energy becomes the kinetic energy of the photoelectron when it leaves the metal

Planck actually didn't realize how revolutionary his work was at the time; he thought he was just fudging the math to come up with the "right answer," and was convinced that someone else would come up with a better explanation for his formula.

photon

hcE hf

λ= = Planck’s

Constant

φ= −KE hf

* Not on Reference Table

320

Practice Questions

1. Determine the energy of a photon that has a frequency of 4.4 × 1014 Hz.

-34 14 -19(6.63 10 )(4.4 10 ) 2.9 10 E hf J s Hz J= = × ⋅ × = ×

2. The beam of light from the previous question is set to shine upon a metal with a work function of 1.8 x 10-19 joules. Calculate the energy of the electrons liberated by the beam of light.

φ− −

−

= −= × − ×= ×

19 19

19

2.9 10 1.8 10

1.1 10

KE hf

KE J J

KE J

3. Which color of light has the most energy?

Violet

4. What type of electromagnetic radiation has the most energy?

Gamma

5. What type of electromagnetic radiation is associated with a photon having 3.5 × 10-23 J of energy?

-2310

-34

3.5 105.3 10

6.63 10

E Jf Hz

h J s

×= = = ×× ⋅

= Microwave

6. The energy of a photon is 2.11 eV. a. Determine the energy of the photon in joules.

-19-191.60 10

2.11 3.38 101

JeV J

eV

× = ×

b. Determine the wavelength of the photon.

-34 8-7

-19

(6.63 10 )(3.00 10 )5.88 10

3.38 10

msJ shc

mE J

λ × ⋅ ×= = = ×

×

c. Determine the type of the electromagnetic wave associated with the photon.

-1914

-34

E 3.38 10 Jf 5.10 10 Hz

h 6.63 10 J s

×= = = ×× i

OR 8 m

14s

-7

3.00 10vf 5.10 10 Hz

5.88 10 m

×= = = ×λ ×

Yellow Light

7. As λ increases, the energy of the photon decreases. 8. Which color of light has photons that travel fastest?

All photons travel at the same speed (3.00 x 108 m/s)

Pop Up Video – National Treasure 1. Average the green light

frequencies.14 14

1 2

14

5.20 10 6.10 10

2 2

5.65 10

avg

avg

f f Hz Hzf

f Hz

+ × + ×= =

= ×

2. Calculate energy

34 14

19

(6.63 10 )(5.65 10 )

3.75 10

E hf J s Hz

E J

−

−

= = × ×= ×

i

3. Calculate wavelength (two options)

8

14

7

3.00 10

5.65 10

5.31 10

msv

f Hz

m

λ

λ −

×= =×

= ×

OR

34 8

19

7

(6.63 10 (3.00 10 )

3.75 10

5.30 10

msJ shc

E J

m

λ

λ

−

−

−

× ×= =×

= ×

i

E = hf � higher f means higher E

E = hf � higher f means higher E

Always use frequency to look up EM types

When it is visible light must state correct color

321

Photon – Particle Collisions

The photoelectric effect demonstrates that a photon, even though it has no mass, has kinetic energy just as a particle does. In 1916, Einstein predicted that the photon should have another particle property, momentum. In 1922, the American physicist Arthur Compton, tested Einstein’s theory by directing X-rays of known wavelength at a graphite target. In 1927, Arthur H. Compton was awarded the Nobel Prize in Physics for his discovery of the particle properties of x-rays.

In the picture below an X-ray photon is striking an electron from a graphite surface. Use the information provided in the pictures to answer the questions below.

What changes do you observe in the photon after the collision?

The wavelength increases, and the frequency decreases (therefore, it also loses E and p).

In any collision between a photon and a particle, these quantities are conserved:

Momentum and energy are conserved (given to electron).

Photon-electron collision experiments give evidence of which nature of light?

Particle

Matter Waves

French physicist Louis de Broglie proved that a photon’s momentum can be represented by the following equation. In 1923 de Broglie suggested that if a wave behaves like a particle. . .

then a particle could behave like a wave.

What wave phenomenon could test this theory?

Diffraction and interference

Using the above equation, the de Broglie wavelength of the particle could be found.

DEMO – cathode ray tube creates electron wind which pushes pin

wheel

His proposal was so extraordinary that it was ignored by other scientists until Einstein read de Broglie’s papers and supported his ideas.

hp =

λ

Which color of light has photons with the greatest momentum?

Since h

p=λ

, the photon with the smallest wavelength has the greatest momentum. Violet.

http://www.colorado.edu/physics/2000/quantumzone/debroglie.htm

* Not on Reference Table

Note: Actually calculating de Broglie wavelength is HONORS Level.

322

A beam of electrons is directed towards a barrier that has two slits in it. The electrons then travel to a screen placed 2.0 m away.

If electrons acted just as particles, what would you expect to see on the screen?

You would only see two bright dots, because only electrons at the opening could pass.

What pattern was seen on the screen? What did this indicate about electrons?

A typical interference pattern was seen. It shows that the electrons behaved similar to waves.

The dual nature of matter:

Matter in motion exhibits particle as well as wave characteristics.

(The wavelengths of ordinary objects, like a thrown baseball, are too small to be detected.)

As the speed of an electron increases, its wavelength decreases.

Mass – Energy Relationship Relativistic Energy Expression - matter and energy are interchangeable, and that a small

amount of mass is made up of a large amount of energy.

• Energy can exist in many forms, and mass energy can be considered to be one

of those forms.

Albert Einstein: “Mass is equivalent to energy, and energy is equivalent to mass.”

Implication:

The fundamental source of all mass in the universe is the conversion of energy into mass.

Electron Beam

Generator

electrons

Phosphor coated

glass screen

Some electrons ricochet off the

edges of the slit.

E=mc2

If light (energy) can act as matter, and matter can act as

energy….than maybe the two are interchangeable.

Although c is the speed of light, this equation doesn't really have anything to do specifically with light. The principle of relativity says that there is a maximum speed, such that nothing can travel faster than that speed. That's what "c" is - the maximum speed. Certain things travel just

at c; light is one of them. Everything else is slower.]

Always use c for this equation!

1.

A b

ase

ba

ll o

f m

ass

0.1

4k

g t

hro

wn

wit

h a

sp

ee

d o

f 4

0 m

/s h

as

a λ

= 1

.2 x

10

-34

m.

To

o s

ma

ll fo

r e

ven

mo

de

rn t

ech

no

logy.

2

. A

n e

lect

ron

mo

vin

g a

t 4

0 m

/s h

as

a λ

= 1

.8 x

10

-5 m

. O

bse

rva

ble

323

Examples of E=mc2

Fission

The splitting of a heavy nucleus into two or more radioactive nuclei, accompanied by the emission of gamma rays, neutrons and a significant amount of energy. Fission usually is initiated by the heavy nucleus absorbing a neutron, but it also can occur spontaneously.

Fusion

A nuclear process whereby several small nuclei are combined to make a larger one whose mass is slightly smaller than the sum of the small ones. The most dramatic consequences of this law are observed in nature, for example in the nuclear fusion process, in which stars like the Sun emit energy and lose mass.

Pair Production and Pair Annihilation

When a positron (anti-particle of electron) finds an electron, they both will annihilate and release two highly energetic gamma rays.

In a quantum process known as “pair production,” an electron and a positron are spontaneously created from energy.

a. How much energy is needed?

E=mc2 = (1.82× 10 -30 kg)(3.00 x 108m/s)2 = 1.64 x 10-13 J

b. Often the two particles collide again and destroy each other in a process known as “pair annihilation.” How much energy is created?

1.64 x 10-13 J

c. What quantities are conserved in these two processes?

Energy and matter and charge

A natural nuclear fission reactor can occur under certain circumstances that mimic the conditions in a constructed

reactor. The only known natural nuclear reactor formed 2 billion years ago in Oklo, Gabon, Africa.

Because protons and neutrons are much more massive than electrons, a greater amount of energy is needed to produce their antiparticle.

Fission Chain Reaction

(Enrico Fermi)

PET Scans – 11C � 11B + e+ + neutrino then e+

and e- � γ

Scientists in the 1930s, using machines that could break apart the nuclear cores of atoms, confirmed Einstein's formula E=mc² . The release of energy in a nuclear transformation was so great that it could cause a detectable

change in the mass of the nucleus.

Need to double mass because two of them

324

Atomic Emission Spectra

By the early 1900s, scientists had made the following observations:

� When a high voltage is passed through the electrodes of an evacuated glass tube filled with

a pure atomic gas, the atoms emit (light) electromagnetic radiation.

� When this light is passed through a very thin slit and then through a prism the light

(electromagnetic radiation) is separated into its component frequencies.

The familiar dispersion of white light is illustrated below:

How is an atomic emission spectrum formed?

� The excited atoms emit light only at certain frequencies, which correlate to specific colors.

The spectral lines in the visible region of the atomic emission spectrum of barium are shown below.

Properties of Spectral Lines

� Spectral lines exist in series in the different regions (infra-red, visible and ultra-violet) of the

electromagnetic spectrum.

� Each element has its own unique “fingerprint” atomic emission spectrum.

325

Spectroscope (Diffraction Grating) - A series of closely spaced parallel slits or grooves that are used

to separate colors of light by interference.

Observe each of the following sources of light through the spectroscope and describe what you see.

Hydrogen

Mercury

Neon

Helium

RED SPREADS – red light ends up the farthest from the light source due to its longer wavelength

We are only observing the spectral lines of radiation emitted in the visible spectrum. Other equipment may reveal radiation in the infrared and ultraviolet ranges or farther.

This is how neon lights work.

CONTINUOUS

PLASMA TV

DEMO – use spectroscopes and evacuated glass tubes - Have students stand by the window and aim the spectroscope at

the sky (bright sunny part) – they see continuous - Have students aim spectroscopes at the ceiling (center on bulb)

– they see thick bands with breaks/gaps - Have students aim spectroscopes at the gas tubes – they see

different color lines for each gas o Start with Neon – easiest to see, and then do Hydrogen and

Mercury. If you run out of time it’s okay to skip helium.

326

Atomic Absorption Spectrum

Emission Spectrum – a unique series of spectral lines emitted by an atomic gas when electrons

return to a lower energy state.

Absorption Spectrum – when an element absorbs a specific series of frequency of electromagnetic

radiation, electrons become excited and jump to higher energy states.

Conclusions:

Atoms only absorb the frequencies that they emit.

Causes of the Atomic Spectra To explain the spectral line puzzle, Bohr came up with a radical model of the atom which had electrons orbiting around a nucleus. Ground state energy level – the lowest energy state which corresponds to the shortest possible

radius

Excited state energy level – any energy level greater than its ground state Ionization energy level – when an atom absorbs sufficient energy to raise an electron to an energy

level so high that the electron is removed from the atom and an ion is formed.

At ordinary temperatures, most electrons are in the ground state, with the electrons relatively close to the nucleus.

Energy levels are quantized; meaning electrons can only move to specific orbits, no where in between.

327

Energy Levels

How does an electron travel to a higher energy level?

It accepts a photon (takes in Energy). How does an electron travel to a lower energy level?

It emits a photon (releases Energy).

Energy Level Diagram – a diagram in which the energy levels of an element are indicated by the

distances of horizontal lines from a zero energy level

• The energy level of an electron that has been completely removed from the atom (n = ∞) is

defined to be 0.00 eV, thus all other energy levels have negative values

http://www.colorado.edu/physics/2000/quantumzone/bohr.html

A photon’s energy is absorbed by an electron in an atom only if the photon’s energy corresponds exactly to an energy-level difference possible for the electron. Excitation energies are different for different elements.

Ephoton = Ei - Ef

Ei = initial energy of electron

Ef = final energy of electron

Ground State

Ionization Level

Emitted photons have positive energy values.

Absorbed photons have negative energy values.

http://wps.prenhall.com/wps/media/objects/610/625137/chaisson/CH.00.002/HTML/CH.00.002.s6.htm

Students need to memorize this!

Like stepping stones on a lake – you can only step on the stones, not in between.

Name of level (listed

on left)

Amount of energy in eV (listed on right)

Excited energy

levels

Absorb E to

travel up

Release E to

travel down

328

Quantum Leap

1. What will happen if hydrogen gas in the ground state is illuminated with light whose photons have an energy of 10.20 eV?

Ei - Ephoton = Ef

(-13.60 eV) – ( -10.20 eV) = -3.40 eV

The electron will jump to the second energy level.

2. What will happen if hydrogen gas in the ground state is

illuminated with light whose photons have an energy of 11.40 eV?

Ei - Ephoton = Ef

(-13.60 eV) – ( - 11.40 eV) = -2.20 eV

The electron will remain in its energy level because

there is no 2.20 eV level.

3. How much energy is needed for an electron to transition from the n = 2 to the n = 3 energy level? Is this energy absorbed or emitted? Will this result in a bright line or dark line in the atomic spectra?

Ephoton = Ei - Ef

= (- 3.40eV) – ( - 1.51eV) = -1.89 eV

Energy is absorbed.

Dark line on absorption spectra

4. An electron in the n = 4 state relaxes to the n = 2 state and emits a photon. How much energy does the photon have?

Ephoton = Ei - Ef

= (- 0.85eV) – ( - 3.40eV) = 2.55 eV 5. A photon whose energy is 1.13 eV is emitted from a hydrogen atom. Determine the energy level

transition that this represents.

n = 6 to n = 3

6. How much energy is needed to ionize an atom in the ground state of hydrogen?

13.60 0.00 13.60photon i fE E E eV eV eV= − = − − = −

7. A hydrogen atom in the ground state absorbs 15.00 electronvolts of energy and is ionized by losing an electron. How much kinetic energy does this electron have after the ionization?

13.60 15.00 1.40i photonKE E E eV eV eV= − = − − − =

Ephoton negative - absorbed

Ephoton negative - absorbed

Ephoton positive - emitted

This is just guess and check to find levels separated by 1.13 eV. Know that is 6 to 3 because energy is emitted. 3 to 6 would be if absorbed

329

8. An electron is excited from the ground state to the n = 3 excited state. How many possible different photons may be emitted as the electron relaxes back down to the ground state?

3 photons may be emitted.

9. What is the energy of each possible photon?

γ1= 12.09 eV or

γ2= 1.89 eV γ3= 10.20 eV

10. Which has the highest frequency?

γ1 has the highest frequency (E=hf)

11. Which has the highest wavelength?

γ2 has the highest wavelength hcE=

λ

Energy Levels of Mercury

12. An electron makes the transition from level f to b in a mercury atom.

a. Was energy gained or released by the atom? How much? Express this energy in joules.

Energy was released by the atom.

Ephoton = Ei - Ef

= (- 2.68eV) – (- 5.74eV) = 3.06 eV (pos. emitted)

-19-191.60 10

3.06 4.90 101

JeV J

eV

× = ×

b. Determine the frequency of the photon.

-19

14

-34

4.90 107.39 10

6.63 10

E Jf Hz

h J s

×= = = ×× ⋅

c. Determine the wavelength of the photon.

8

7

14

3.00 104.06 10

7.39 10

msc

mf Hz

λ −×= = = ×

× OR

34 87

19

(6.63 10 )(3.00 10 )4.06 10

4.90 10

msJ shc

mE J

λ−

−−

× ×= = = ×

×i

d. Determine the color of the photon.

Violet This is the cause of the violet band seen with the spectroscope.

1. n = 3 to n = 1

E

= (-1.51eV) - (- 13.60 eV)

= 12.09 eV

2. n = 3 to n = 2

E

= (-1.51eV) - (- 3.40 eV)

= 1.89 eV

3. n = 2 to n = 1

E

p i f

p i f

p i f

E E

E E

E E

= −

= −

= − = (-3.40eV) - (- 13.60 eV)

= 10.20 eV

330

Doppler Shift Revisited

Redshift

The light of an object moving away from an

observer is shifted toward a longer wavelength, or

toward the color red.

Blueshift

The light of an object moving toward an observer is

shifted toward a shorter wavelength, or toward the

color blue.

NOTE – the color is not RED or BLUE, it is only shifted toward that end of the light spectrum

What can scientists tell about the universe using the Doppler Shift? Based upon the degree of shift they can:

• Measure the speed and direction of:

o Moving stars

o Moving galaxies

o Star surfaces (expanding/contracting)

• Measure the period of a binary star system and use that information to

calculate the mass of the stars (The reverse process from the Kepler’s Law lab done

in Universal Gravitation/Kepler’s Laws chapter)

• Determine the direction of rotation for stars and galaxies

So, using one simple physical phenomenon -- the Doppler Shift -- that you can hear for yourself on any city street, scientists can make discoveries about the speeds, masses, and behavior of stars as close as our Sun or as distant as other galaxies, and study the properties of those galaxies to find out the structure of the Universe. Think of that, next time a fire truck goes by!

Extremely careful measurements of nearby stars can determine their relative speeds with a precision as small as 10 meters per second. Analyzing a large number of nearby stars shows that our Sun and its neighbors orbit the distant center of our Milky Way galaxy with a velocity of 250 km/sec. We're about 26,000 light years from the center of the Galaxy, and so it'll take 220 million years for us to complete an orbit. We can also tell that the stars nearer the center of the Galaxy rotate faster, so we're being 'passed' by those stars nearer the center, and 'overtaking' those stars that orbit further from the center of the Galaxy.

Certain types of stars known as CEPHEID VARIABLES have atmospheres that swell and shrink periodically. Using the Doppler

technique, we can tell that such a star's surface may be moving at speeds up to 50 km/sec

The equator at the Sun's east limb is approaching us at 2 km/sec, and the west limb is retreating from us at the same speed. Some stars have equatorial speeds of 400 km/sec; if they spun any faster, they would break up!

When we look at the spectra of other galaxies and map their velocities, we find that on average, all galaxies are speeding away from each other, with very high redshifts. (There are exceptions, where galaxies are close enough to be drawn together by their gravities.) The Doppler Shift tells us that the universe as a whole is expanding. What's more, galaxies at greater distances ('higher redshifts') are speeding away more quickly -- just as you'd expect in the aftermath of a giant

explosion: the Big Bang. And it now looks as if the expansion of the universe is accelerating

331

Atomic and Nuclear Structure

Atomic Structure Nucleon:

Any particle that comprises the nucleus.

ex - the neutron or proton.

What holds the nucleus together?

The strong nuclear force, which is an attractive force between protons and neutrons.

Nuclear Structure

Universal Mass unit – ( u ) – an atomic mass unit defined as 1 / 12th the mass of an atom of

carbon-12

Particle Electric Charge (C) Mass in Kilograms

(kg) Mass in Universal Mass

Units (u)

Electron -1.60 × 10 -19 9.11 × 10 -31 5.49 × 10 -4 (0.000549)

Proton +1.60 × 10 -19 1.67 × 10 -27 1.0073

Neutron 0 1.67 × 10 -27 1.0087

1. What is the charge on a lithium nucleus that consists of 3 protons and 4 neutrons?

3(+1.60 x 10-19 C) = + 4.80 x 10 -19 C

2. What is the mass of the same lithium nucleus? Calculate it in both kilograms and universal mass units.

7(1.67 x 10-27 kg) = 1.17 x 10 -26 kg

3(1.0073 u) + 4(1.0087 u) = 7.0567 u

3. How much energy would be released if this lithium nucleus were converted completely into energy?

E=mc2 = (1.17 x 10 -26 kg)(3.00 x 108m/s)2 = 1.05 x 10-9 J

Must use kg!

Proton and neutron have same mass to 3 s.f., but neutron is slightly larger, shown with mass to 5 s.f.

332

Mass Defect and Binding Energy

The mass of a stable atomic nucleus is less than the sum of the masses of the individual nucleons Why?

When nucleons come together to form a nucleus, mass is converted into energy that bonds the nucleons.

Mass Defect - the difference between the mass of a nucleus and the sum of the masses of the

nucleons that form the nucleus.

Units – universal mass unit (u)

Binding Energy - the energy that is required to combine or separate the nucleons.

Units – Mega-electronvolt (MeV)

_____________Binding Energy_____________ = _____________Mass Defect_____________

1. An alpha particle (a helium nucleus) consists of two protons and two neutrons and has a mass of 4.0016 u. The mass of a proton is 1.0073 u and the mass of a neutron is 1.0087 u.

a. Find the mass defect of the helium nucleus.

( ) ( )2 1.0073 2 1.0087 –4.0016

.0304

defect protons neutrons nucleum

defect

defect

m m m m

m u u u

m u

= + −

= +

=

b. Find the binding energy of the helium nucleus in MeV.

29.31x10 MeV.0304u =28.3 MeV

1u

2. A deuterium nucleus has a mass that is 1.53 x 10-3 universal mass units less than the mass of its components. How much energy does this represent?

2-3 9.31x10 MeV

1.53x10 u =1.42 MeV1u

Mass in: Use equation: Energy in:

Kilograms (kg) E = mc2 Joules (J)

Universal mass units (u)

1 u = 931 MeV MeV

Binding Energy equals Mass Defect

1 u = 931 MeV m defect = m proton + m neutron – m nucleus

*Not on Reference Table

333

Early Models of the Atom

Aristotle Democritus Thomson Rutherford Bohr Cloud Model

Fire

Water Air

Earth

Matter is comprised of atoms. Atomos = indestructible

Uniform distribution of positive and negative charge.

Plum Pudding

Mostly empty space, dense positive nucleus, orbiting electrons Thin gold foil

Electrons orbit at quantized or specific orbitals

Regions or clouds in which electrons would most likely be found

The Standard Model

Standard Model - a theory used to explain the existence of all the particles that have been observed

and the forces that holds atoms together or leads to their decay.

The Four Fundamental Forces of Nature

Electro-weak Force - at extremely high energies, the differences between the weak force and the

electromagnetic force become less significant and the two forces become indistinguishable and

strong.

Four Fundamental

Forces

Strong Nuclear Force

Binds quarks together inside

protons and neutrons

Electromagnetic Force

Occurs between any two particles that have electric charge

Responsible for governing electron orbits and chemical

processes

Weak Force

Responsible for radioactive

decay

Gravitational Force

Attractive force between any two particles that have

energy/mass

“glue”

Is negligible beyond distance of nucleus

Though 400 stable nuclei exist, there are hundreds of unstable nuclei.

Can be natural or artificial.

Α, β, γ are

emitted.

Although the details of the Standard Model are very

complex, the model’s essential elements are very basic.

Probability Function –

Schrödinger & Heisenberg

In the 60’s, Physicists used a branch of math called Group Theory to show how the weak and

electromagnetic force could combine.

Demo – Turn on a fan and show the blades can’t be distinguished because moving too fast – electrons move too fast to determine location

Gold foil – “like shooting a shotgun at a tissue and having the bullet bounce back”

334

Properties of Forces

Scientists knew that atoms did not actually touch, but were confused as to how they interacted. From this concept, scientists introduced the idea of elementary particles that carry the force from one atom to another.

Force Relative Strength

Range of Force Force Carrier Mass Charge

Strong (Nuclear) 1 ~ 10-15 m Gluon 0 0

Electromagnetic 10-2 Infinite Photon 0 0

Weak 10-13 <10-18 m

W+ boson

W- Boson

Z Boson

80.6 GeV

80.6 GeV

91.2 GeV

+e

-e

0

Gravitational 10-38 Infinite Graviton 0 0

Classification of Matter

Quark – the smallest known building blocks of matter.

• Never occur alone.

• Always found in combinations with other quarks.

There are six types (flavors) of quarks.

Up (u) Down (d) Charm (c) Strange (s) Top (t) Bottom (b)

Lepton – a class of subatomic particles including the electron which are not influenced by the

strong force

Antiparticle - a particle having mass, lifetime, and spin identical to associated particle, but having

opposite charge

• If an antiparticle and the corresponding particle of ordinary matter get too close together,

both will disappear in a burst of energy.

� Example – anti-up quark (ū)

Antimatter - material consisting of atoms that are composed of antiprotons, antineutrons, and

positrons

2nd and 3rd gen exist for a short time

Heavier than first generation

Tend to decay into first generation

A force can be thought of as mediated by an exchange of particles.

↓ Only estimates (depends on assumed separation distance)

Quarks interact strongly with one another. They are unique because of

their fractional charge.

The electron is no longer thought

to be the smallest charge.

There are no anti-force carriers to best of our knowledge.

An anti-neutron is made of anti-quarks – lack of charge does not matter

First gen are most stable – see more

Finnegan’s Wake

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Particles of the Standard Model

1. What is e ?

The charge of an electron (1.60 x 10-19 C)

2. What is the charge on the positron? on the anti-down quark?

The charge on the positron is + 1.60 x 10-19 C. On the anti-

down quark is + 1/3 e. (5.33x10-20C)

3. What are the quark composition, charge and classification of each of the following particles?

Proton Antiproton Neutron Antineutron Electron Positron

uud ūūđ udd ūđđ e ē

+1 e - 1 e 0 e 0 e - 1 e + 1 e

Baryon Anti-Baryon Baryon Anti-Baryon Lepton Antilepton

Matter

Hadrons Any particle composed of quarks.

Uses all 4 fundamental forces

Ex. – protons & neutrons.

Leptons The most basic building blocks of matter

Does NOT use strong force Ex – electrons

Baryons Mesons

three quarks quark and antiquark

Leptons interact weekly

with one another.

Proton, neutron, lambda, sigma Pions, kaons, D particles

In 1963, two different scientists each proposed independently that Hadrons have a more

elementary structure.

Quarks other than u and d are needed to construct rare forms of matter.

All particles can be classified

into two broad categories.

Heaviest Heavier

Lightest

Abnormal Matter

All unstable

Show reference tables with the two charts – classification of matter and

particles of standard model

In 1932, scientists though protons and electrons were elementary particles because they were stable. In 1945, experiments at particle accelerators

demonstrated that new particles are formed in high energy collisions between 2 known particles. (New particles: unstable, short lived) 300 new particles

Students need to memorize that a proton is uud and a neutron is udd

How are all of these unstable particles created? Stable particles collide and some of their KE is converted into mass to make new particles. Eventually the new particles will turn back into the stable particles.

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4. What is the electric charge and classification of a particle having a

quark composition of s_

b ?

1 13 3

( ) ( ) 0 Mesone e e− + + =

5. A particle has a quark composition of ucb. What charge does the particle have

and what is its classification?

2 2 13 3 3

( ) ( ) ( ) 1 Baryone e e e+ + + + − = +

6. A particle has a quark composition of d _

t . What charge does the particle have and what is

its classification?

1 23 3

( ) ( ) 1 Mesone e e− + − = −

7. What are the possible charges a meson can have?

1 13 3

( ) ( ) 0e e e− + + = 2 23 3

( ) ( ) 0e e e− + + = 2 13 3

( ) ( ) 1e e e− + − = − 2 13 3

( ) ( ) 1e e e+ + + = +

Since it is a quark and anti-quark, it will range between -1e and +1e, integers only (no fractions)

8. What are the possible charges a baryon can have?

1 1 13 3 3

( ) ( ) ( ) 1e e e e− + − + − = − 2 2 23 3 3

( ) ( ) ( ) 2e e e e+ + + + + = + 2 1 13 3 3

( ) ( ) ( ) 0e e e e+ + − + − = 2 2 13 3 3

( ) ( ) ( ) 1e e e e+ + + + − = +

Since it is three, it will range between -1e and +2e, integers only (no fractions)

Bubble Chambers

Bubble Chamber - A device for detecting charged particles and other radiation by means of tracks of bubbles left in a chamber filled with liquid hydrogen or other liquefied gas

• Particles traveling at extremely high speeds collide with each other

• Some of the kinetic energy converts into mass and creates the new particles

It was invented in 1952 by Donald Glaser. The bubble chamber consists essentially of a sealed chamber to be filled with a liquefied gas and constructed so that the pressure inside can be reduced quickly. The liquid is originally at a temperature just below its boiling point. When the pressure is reduced, the boiling point becomes lowered so that it is less than the temperature of the liquid, leaving the liquid superheated. When a charged particle passes through this superheated liquid, it leaves a trail of tiny gas bubbles that can be illuminated and photographed. The track of a charged particle can be used to identify the particle and to analyze complex events in which it may be involved. If a magnetic field is present, the tracks of the particles will be curved, positively charged particles curving in one direction and negatively charged particles curving in the opposite direction. The degree of curvature depends on the mass, speed, and charge of the particle. Neutral particles can be detected indirectly by applying various conservation laws to the events recorded in the bubble chamber or by observing their decay into pairs of oppositely charged particles.

Have students use their reference tables and the

Particle of the Standard Model chart while answering these.

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Special Relativity

For everyday observations, Newton’s laws of motion provide good approximations for describing and predicting motion. If the speed of a particle approaches the speed of light however, a different approach is required to interpret motion. This approach was developed by Albert Einstein in 1905. Einstein’s Special Theory of Relativity is based on two postulates:

1. The laws of physics are the same in all inertial reference frames.

• Inertial reference frame means the reference frames are moving at constant velocity

relative to one another.

2. The speed of light is constant in all reference frames, despite any relative motion between

an observer and the light source.

As a result of this theory there are three main consequences: Length Contraction – the length of an object contracts in the

direction of motion when measured by a stationary observer.

• The faster the object travels, the shorter it becomes. Time Dilation – time slows down at high speeds

• Moving clocks run more slowly than stationary clock. The faster the clock moves, the slower the time runs.

• Each observer believes their time is the normal time. Relativistic Mass – as the velocity of an object approaches the speed of light, the mass increases

toward infinity

Twin Paradox - The astronaut twin goes on a journey to a distant star in a very fast rocket ship. The scientist twin stays home. When the astronaut twin returns home, who is older?

• According to the scientist, he is at rest while the astronaut was moving, so the astronaut ages more slowly and is younger.

• According the astronaut, he is at rest while the scientist was moving, so the scientist ages more slowly and is younger.

• Resolution: o The astronaut’s frame of reference is non-inertial (it accelerates), so he really is

the one moving at high speeds and his time will run slower. The astronaut is younger.

Einstein’s theory does not replace Newton’s laws. They are a special case when the

speeds do not approach the speed of light.

As the mass of an object increases, its kinetic energy increases. It would take an infinite amount of energy to accelerate a massive object

to c. Scientist doubt anything will be able to exceed c for this reason.

Can never cross the vertical line which represents speed of light, c