QUANTUM AND NUCLEAR PHYSICS

Mark LesmeisterPearland ISD Physics

Acknowledgements

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PARTICLES OF LIGHT

Infrared Videos: Bats Emerging from Caves

Videos from Boston University Center for Ecology and Conservation Biology, http://www.cs.bu.edu/fac/betke/research/bats/videos.html

Blackbody Radiation

All objects emit electromagnetic radiation.

The frequencies of this radiation and the amount emitted depend on the temperature of the object.

“Room temperature” objects emit infrared frequencies.

Very hot objects (like glowing coals) emit visible radiation.

The universe, which has a temperature of 3 Kelvin, is awash with microwave radiation.

Source: Darth Kule, “Black-body.svg”, http://en.wikipedia.org/wiki/File:Black_body.svg. Retrieved May 14, 2010. Graphic is public domain.

Quantization of Energy In the 19th

century, experiments were conducted to measure the blackbody radiation emitted at each wavelength of light.

Source: Darth Kule, “Black-body.svg”, http://en.wikipedia.org/wiki/File:Black_body.svg. Retrieved May 14, 2010. Graphic is public domain.

Quantization of Energy The wave-

theory of EM radiation did not agree with the experimental results for blackbody radiation.

Source: Darth Kule, “Black-body.svg”, http://en.wikipedia.org/wiki/File:Black_body.svg. Retrieved May 14, 2010. Graphic is public domain.

Quantization of Energy

In 1900, Max Planck developed a new theory that assumed energy isn’t emitted in any amount, but only in packets, called “quanta”.

This “quantum” theory agreed with the blackbody experiments.

Experimental data points based on a graph from Wilson,Buffa and Lou, College Physics, Pearson Education Inc., 2010

Planck’s Equation

Planck’s equation relates the energy of a quantum of light with the frequency of light.

Energy = Planck’s constant x frequency

In atoms, energy is measured in electron volts (eV) 1 eV = 1.60 x 10-19 J h=4.14 x 10-15 eV-s

hfE

Photon Practice 1

A certain radio station broadcasts a radio wave of 100 MHz and 30,000 W power.

How many photons does the station emit per second?

Answer: 4.5 x 1029 photons/second

Photon Practice 2 Two monochromatic light beams, one red and

one green, have the same intensity and cover the same area. How does the energy of each photon and the number of photons in each beam compare?

Photon Energy # per Second A) Same Same B) Greater for red Less for red C) Greater for redGreater for red D) Less for red Less for red E) Less for red Greater for red

THE PHOTOELECTRIC EFFECT

The Photoelectric Effect When light strikes a

metal surface, it will give off electrons.

The Photoelectric Effect If light is a wave,

then a light beam that has greater intensity (greater energy) should cause the electrons given off to have more energy.

A more intense light beam causes more electrons to be emitted, but they all have the same energy.

The Photoelectric Effect Einstein explained

the photoelectric effect by assuming that light was made of particles.

A more intense light beam has more photons, but each carries the same energy.

Thus, more intense light would produce more electrons, with the same energy.

The Photoelectric Effect

Quantum Theory of Light and the Photoelectric Effect When a photon strikes a metal plate, it

transfers energy to the electrons in the plate.

If an electron acquires enough energy, it can be ejected from the plate. The energy necessary to eject an electron is

called the “work function” of the metal. The kinetic energy of the electrons will be

the energy of the photon minus the work function. ionWork Funct hfKE

Photoelectric Effect: Practice

A certain beam of light has photons with 5 eV of energy. When this light strikes a metal plate, electrons with 3 eV of kinetic energy are released. What is the work function of the metal?

Answer: 2 eV

The Cutoff Frequency

The Cutoff Frequency

The cut-off frequency is the frequency that produces photons of just enough energy to be emitted, i.e. equal to the work function.

Photons with less energy will not be able to eject electrons.

Work Function = h fCutoff

Wave Particle Duality In some

experiments, such as blackbody radiation and the photoelectric effect, light acts like a particle (called a photon).

In others, like double slit interference and thin film interference, light acts like a wave.

Light never appears as both in the same experiment.

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THE QUANTUM THEORY OF LIGHT AND THE ATOM

Review- Electrical Potential Energy An atom’s electrons

are attracted to its nucleus.

It requires energy to separate them.

The farther away an electron is from the nucleus, the greater the energy.

Energy Levels

The electrons in an atom occupy discrete energy levels. These levels

are determined by the type of atom involved.

An electron gains or loses energy when transitioning between levels.

Energy Levels

We use an energy level diagram to represent the levels.

Absorption When an atom absorbs a photon of light, an

electron “jumps” from a lower energy level to a higher energy level. Only photons with the right amount of

energy will cause an electron to jump to a higher level.

Absorption When an atom absorbs a photon of light, an

electron “jumps” from a lower energy level to a higher energy level. Only photons with the right amount of

energy will cause an electron to jump to a higher level.

Emission Electrons at higher levels can jump back

to a lower energy level by emitting a photon. The frequency of the emitted photon is

determined by the energy that the electron gave up.

Energy Levels Electrons at

higher levels can jump back to a lower energy level by emitting a photon. The frequency

of the emitted photon is determined by the energy that the electron gave up.

Emission Spectra Since the energy levels are different for

each type of atom, the wavelengths of light given off by the excited electrons jumping back down are different for each type of atom.

We can thus identify the atoms by the colors of light they emit.

The pattern of colors is called an emission spectrum.

Emission Spectra

H

Fe

Source: Adrignola, “Emission spectrum-H.svg”Yttrium91, “Emission spectrum-Fe.svg”Wikipedia Commons, public domain

Absorption Spectra

When light containing all wavelengths passes through a gas, the same wavelengths of light that appear in that gas’ emission spectrum will be absorbed by the gas.

Source: Maureen Gebruiker, “Fraunhofer lines.svg” Wikipedia Commons, public domain

CONSEQUENCES OF QUANTUM MECHANICS

Double Slit Experiment for Electrons

We can carry out a double slit experiment for electrons just like Thomas Young did for light.

But electrons are particles, so they won’t produce an interference pattern, right?

Double Slit Experiment for Electrons

Source: Belsazar, Double-slit experiment results Tanamura 2.jpg, Wikipedia Commons, Creative Commons Attribution-Share Alike 3.0 Unported license.

Double Slit Experiment for Electrons

Electrons interfere with each other, just like waves.

If we cover up one slit, the wave-like behavior goes away.

The wave-particle duality of matter Particles of matter, such as

electrons, atoms, etc., can also behave like a wave in some experiments.

These matter waves are called de Broglie waves. The wavelength of these waves is

given by the equation l = h/p . The frequency is given by the

equation f=E/h

NUCLEAR PHYSICS

The Nucleus

An atomic nucleus consists of protons and neutron.

When we want to specify a specific isotope, we write the mass number and atomic number.

He42

neutrons ofnumber

protons ofnumber number atomic

nucleons ofnumber number mass

N

Z

A

NZA

Units of Mass and Energy in Nuclear Physics In nuclear

physics, mass is usually stated in terms of atomic mass units, or u. 1 u = 1.660 X 10-

27 kg Energy is usually

stated in electron-volts, or eV.

Particle

m (kg) m (u)

Proton 1.673 x 10-

27

1.007276

Neutron

1.675 x 10-

27

1.008665

Electron

9.109 x 10-

31

.000549

1 eV= 1.602 X 10-19 J

Mass-Energy Equivalence

Energy and mass are equivalent.

Einstein’s equation shows how much energy a quantity of mass corresponds to.

2

2

light) of (speed mass Energy

mcE

Mass-Energy Equivalence

Energy and mass are equivalent.

Einstein’s equation shows how much energy a quantity of mass corresponds to.

Particle m (kg) E (MeV)

Proton 1.673 x 10-27 938.3

Neutron 1.675 x 10-27 939.6

Electron 9.109 x 10-31 0.5110

1 u = 931.5 MeV

The Strong Force

The electric force would cause the protons in a nucleus to repel each other.

The strong force is an attractive that overcomes the electric repulsion over small distances.

Both protons and neutrons attract by the strong force.

Neutrons help stabilize the nucleus.

Elements with Z>83 do not have stable nuclei.

Fundamental Forces

Force Strength* Range Field Particle

Strong Nuclear 1 ~ 1 fm = 10-15 m

gluon

Electromagnetic

10-2 Infinite (1/r2) photon

Weak Nuclear 10-13 < 10-3 fm W+,W-, and Z

Gravity 10-38 Infinite (1/r2) graviton

* Since the forces involve different quantities and vary with distance, their strength is not a simple comparison. The answer on the homework reverses the weak nuclear and electromagnetic force relative strength.

Binding Energy The total energy

or mass of a stable nucleus is less than the mass of the individual nucleons.

The difference is called the binding energy, Ebind

=+ Binding Energy

Mass Defect Since mass and

energy are equivalent, the difference can also be expressed in terms of mass.

The difference in mass is called the mass defect, Δm

=+ Binding Energy

Nuclear Physics Questions 1 & 2 Determine

the mass defect and binding energy of deuterium.

Determine the mass defect and binding energy of helium.

Particle m (u) E (MeV)

Proton 1.007825 938.3

Neutron 1.008665 939.6

D 2.014102

He 4.002602

1 u = 931.5 MeV

Binding Energy and Nuclear Reactions Nuclear reactions

involve the nuclei of atoms.

If a rearrangement of protons and neutrons in a nucleus or nuclei results in a greater binding energy, the reaction will release energy.

Energy

Nuclear Physics Question 3 Determine

the energy “released” when 2 deuterium combine to form a helium nucleus.

Particle m (u) E (MeV)

Proton 1.007825 938.3

Neutron 1.008665 939.6

D 2.014102

He 4.002602

1 u = 931.5 MeV

Nuclear stability

The attraction of the strong force results in lower energy/nucleon for light nuclei.

Because the range of the strong force is limited, beyond a certain size, binding energy/nucleon increases. Source: Fastfission, Wikipedia,

public domain

Fission In nuclear fission, heavy nuclei split

into lighter nuclei.

Fission This may result in a chain reaction.

A nuclear reactor uses a controlled chain reaction.

The first “atomic” bombs were fission bombs.

Fusion Light nuclei can

undergo fusion. Fusion is the

nuclear reaction that powers the sun.

Researchers are trying to develop a fusion reactor that releases more energy than it uses.

Source: Wykis, “Deuterium-tritium fusion.svg” Wikipedia Commons, public domain

Nuclear Physics Question 3

Correct statements about the binding energy of a nucleus include which of the following:

I) It is the energy needed to separate the nucleus into its individual nucleons.

II) It is the energy liberated when the nucleus is formed from the original nucleons.

III) It is the energy equivalent of the apparent loss of mass of its nucleon constituents.

A) I only. B) III only. C) I and II only. D ) II and III only. E) I, II, and III

NUCLEAR RADIATION

What is your radiation dose?

Calculate Your Radiation Dose | Radiation Protection | US EPA

Nuclear Decay An unstable

nucleus can break apart into other particles, releasing energy.

This process occurs naturally in hundreds of types of nuclei.

+ + Energy

Nuclear Radiation Three types of radiation are emitted in

radioactive decay.

Particle Symbol Composition Charge Effect on Parent

Alpha 2 protons, 2 neutrons (He nucleus)

+2 Less mass, new element

Beta electron

positron

-1

+1

~same mass, new element

Gamma photon 0 Energy loss

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Uses of nuclear radiation Carbon dating Chemical tracing Radiation therapy Food irradiation Sterilization of

medical equipment

Non-destructive testing

Smoke detectors Security scanning Nuclear power

n10

Carbon Dating

Some atmospheric carbon is C-14, produced by cosmic rays.

N147C14

6H11

HCNn 11

146

147

10

Carbon Dating

This carbon-14 naturally decays to nitrogen with beta decay.

eNC 01

147

146

C146-N

147

Radioactive Decay Question 1

H)(deuteron a (E)

He).( nucleus helium a (D)

electron.an (C)

neutron. a (B)

proton. a (A)

plusRn into decays Ra

21

42

22286

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