Transcript Nuclear Physics

Nuclear Physics
Quantum Physics

Physics on a very small (e.g., atomic) scale is
“quantized”.

Quantized phenomena are discontinuous and
discrete, and generally very small.

Quantized energy can be thought of as existing in
packets of energy of specific size.

Atoms can absorb and emit quanta of energy, but
the energy intervals are very tiny, and not all energy
levels are “allowed” for a given atom.
Light: Ray

We know from geometric optics that light
behaves as a ray. This means it travels in a
straight line.

When we study ray optics, we ignore the
nature of light, and focus on how it behaves
when it hits a boundary and reflects or
refracts at that boundary.
Light: Wave

We will frequently use one equation from
wave optics in quantum optics.

c = λf
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c: 3 x 108m/s (the speed of light in a vacuum)
λ: wavelength (m) (distance from crest to crest)
f: frequency (Hz or s-1)
Light: Particle

Light has a dual nature. In addition to behaving as a
wave, it also behaves like a particle.

It has energy and momentum, just like particles do.
Particle behavior is pronounced on a very small
level, or at very high light energies.
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A particle of light is called a “photon”.
Photon Energy
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The energy of a photon is calculated from it
the frequency of the light.
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E = hf
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E: energy (J or eV)
h: Planck’s constant
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6.625×10-34 J s
4.14 ×10-15 eV s
f: frequency of light (s-1, Hz)
Check

Which has more energy in its photons, a very
bright, powerful red laser or a small key-ring
red laser?

Which has more energy in its photons, a red
laser or a green laser?
Electron Volts

The electron-volt is the most useful unit on
the atomic level.

If a moving electron is stopped by 1 V of
electric potential, we say it has 1 electron-volt
(or 1 eV) of kinetic energy.

1 eV = 1.602×10-19 J
Problem

What is the frequency and wavelength of a photon whose energy is
4.0 x 10-19 J?
Problem

How many photons are emitted per second by a He-Ne laser that
emits 3.0 mW of power at a wavelength of 632.8 nm?
Atomic Transitions
Energy Levels

This graph shows
allowed quantized
energy levels in a
hypothetical atom.

The more stable states
are those in which the
atom has lower energy.

The more negative the
state, the more stable
the atom.
Energy Levels

The highest allowed energy is
0.0 eV. Above this level, the
atom loses its electron. This
level is called the ionization
level.

The lowest allowed energy is
called the ground state. This
is where the atom is most
stable.

States between the highest
and lowest state are called
excited states.
Energy Levels

Transitions of the
electron within the atom
must occur from one
allowed energy level to
another.

The electron CANNOT
EXIST between energy
levels.
Photon Absorption

When a photon of light is absorbed by an atom, it
causes an increase in the energy of the atom.

The photon disappears.

The energy of the atom increases by exactly the
amount of energy contained in the photon.

The photon can be absorbed ONLY if it can produce
an “allowed” energy increase in the atom.
Photon Absorption

When a photon is
absorbed, it excites
the atom to higher
quantum energy
state.

The increase in
energy of the atom is
given by ΔE = hf.
0eV
-10eV
Absorption Spectra

When an atom absorbs photons, it removes the
photons from the white light striking the atom,
resulting in dark bands in the spectrum.

Therefore, a spectrum with dark bands in it is called
an absorption spectrum.
Absorption Spectra

Absorption spectra
always involve
atoms going up in
energy level.
0eV
-10eV
Photon Emission

When a photon of light is emitted by an atom, it
causes a decrease in the energy of the atom.

A photon of light is created.
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The energy of the atom decreases by exactly the
amount of energy contained in the photon that is
emitted.

The photon can be emitted ONLY if it can produce
an “allowed” energy decrease in an excited atom.
Photon Emission

When a photon is
emitted from an
atom, the atom drops
to lower quantum
energy state.

The drop in energy
can be computed by
ΔE = hf.
0eV
-10eV
Emission Spectra

When an atom emits photons, it glows! The photons
cause bright lines of light in a spectrum.

Therefore, a spectrum with bright bands in it is
called an emission spectrum.
Emission Spectra

Emission spectra
always involve
atoms going down
in energy level.
0eV
-10eV
Problem

What is the frequency and wavelength of the light that will cause
the atom shown to transition from the ground state to the first
excited state? Draw the transition.
Problem

What is the longest wavelength of light that when absorbed will
cause the atom shown to ionize from the ground state? Draw the
transition.
Problem

The atom shown is in the second excited state. What frequencies
of light are seen in its emission spectrum? Draw the transitions.
The Photoelectric Effect
Absorption

We’ve seen that if you
shine light on atoms, they
can absorb photons and
increase in energy.

The transition shown is the
absorption of an 8.0 eV
photon by this atom.

You can use Planck’s
equation to calculate the
frequency and wavelength
of this photon.
Extra Energy

Now, suppose a photon with TOO MUCH
ENERGY encounters an atom?

If the atom is “photo-active”, a very
interesting and useful phenomenon can
occur…

This is called the Photoelectric Effect.
Photoelectric Effect

Some “photoactive” metals can
absorb photons that not only
ionize the metal, but give the
electron enough kinetic energy to
escape from the atom and travel
away from it.
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The electrons that escape are
often called “photoelectrons”.

The binding energy or “work
function” is the energy necessary
to promote the electron to the
ionization level.

The kinetic energy of the electron
is the extra energy provided by
the photon.
Photoelectric Effect
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Photon Energy = Work Function + Kinetic
Energy
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hf = Ф + Kmax
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Kmax = hf – Ф
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Kmax: Kinetic energy of “photoelectrons”
hf: energy of the photon
Ф : binding energy or “work function” of the metal.
Problem

Suppose the maximum wavelength a photon can have and still eject
an electron from a metal is 340 nm. What is the work function of the
metal surface?
Photoelectric Effect

Suppose you collect Kmax and frequency data
for a metal at several different frequencies.
You then graph Kmax for photoelectrons on yaxis and frequency on x-axis. What
information can you get from the slope and
intercept of your data?
The Photoelectric Effect

The Photoelectric Effect experiment is one of the
most famous experiments in modern physics.

The experiment is based on measuring the
frequencies of light shining on a metal (which is
controlled by the scientist), and measuring the
resulting energy of the photoelectrons produced by
seeing how much voltage is needed to stop them.

Albert Einstein won the Nobel Prize by explaining
the results.
Photoelectric Effect Diagram
Photoelectric Effect

Voltage necessary to stop electrons is independent
of intensity (brightness) of light. It depends only on
the light’s frequency (or color).
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Photoelectrons are not released below a certain
frequency, regardless of intensity of light.

The release of photoelectrons is instantaneous,
even in very feeble light, provided the frequency is
above the cutoff.
Photoelectric Effect

The kinetic energy of photoelectrons can be
determined from the voltage (stopping
potential) necessary to stop the electron.

If it takes 6.5 Volts to stop the electron, it has
6.5 eV of kinetic energy.
Momentum
Mass of a Photon

Photons do not have “rest mass”. They must travel
at the speed of light, and nothing can travel at the
speed of light unless its mass is zero.

A photon has a fixed amount of energy (E = hf).

We can calculate how much mass would have to be
destroyed to create a photon (E=mc2).
Problem

Calculate the mass that must be destroyed to
create a photon of 340nm light.
Photon Momenum


Photons do not have
“rest mass”, yet they
have momentum! This
momentum is evident in
that, given a large
number of photons,
they create a pressure.
A photon’s momentum
is calculated by
E
p
c
Proof of Photon Momentum

Compton scattering
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Proof that photons have momentum.
High-energy photons collided with electrons
exhibit conservation of momentum.
Work Compton problems just like other
conservation of momentum problems

except the momentum of a photon uses a different
equation.
Problem

What is the momentum of photons that have
a wavelength of 620 nm?
Problem

What is the frequency of a photon that has
the same momentum as an electron with
speed 1200 m/s?
Matter Waves
Matter Waves

Waves act like particles sometimes and
particles act like waves sometimes.

This is most easily observed for very
energetic photons (gamma or x-Ray) or very
tiny particles (elections or nucleons)
Energy

A moving particle has kinetic energy


A particle has most of its energy locked up in its
mass.
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E = K = ½ mv2
E = mc2
A photon’s energy is calculated using its frequency

E = hf
Momentum

For a particle that is moving


For a photon
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p = mv
p = h/λ
Units?
Wavelength

For a photon
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λ = c/f
For a particle, which has an actual mass, this
equation still works


λ = h/p where p = mv
This is referred to as the deBroglie wavelength
Matter Wave Proof
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Davisson-Germer Experiment

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Verified that electrons have wave properties by
proving that they diffract.
Electrons were “shone” on a nickel surface and
acted like light by diffraction and interference.
Problem

What is the wavelength of a 2,200 kg
elephant running at 1.2 m/s?
Nuclear Decay
Notation
Atomic Mass
(Protons + Neutrons)
209
83
Atomic Number
(Protons)
Bi
Element
Isotopes

Isotopes have the same atomic number and
different atomic mass.

Isotopes have similar or identical chemistry.

Isotopes have different nuclear behavior.
Half Life

The time required for one-half of an element’s
to decay.
Nuclear Particles
1
1
1
0
p
n
0
1
e
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Proton
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Neutron
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Charge: +e
Mass: 1.66 x 10-27 kg (1 amu)
Charge: 0
Mass: 1.66 x 10-27 kg (1 amu)
Electron


Charge: -e
Mass: 9.1 x 10-31 kg (1/2000 amu)
Decay
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Nuclear Decay: a spontaneous process in which an
unstable nucleus ejects a particle and changes to
another nucleus.
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Alpha decay
Beta decay
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Beta Minus
Positron
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Fission: a nucleus splits into two fragments of
roughly equal size.

Fusion: Two nuclei combine to form another
nucleus.
Decay
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Alpha decay
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Beta decay
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A nucleus ejects an alpha particle, which is just a
helium nucleus.
A nucleus ejects a negative electron.
Positron decay
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A nucleus ejects a positive electron.
Alpha Decay
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Alpha particle (helium nucleus) is released.

Alpha decay only occurs with very heavy
elements.
Beta Decay

Beta decay occurs when a nucleus has too
many neutrons for the protons present.

A neutron converts to a proton. An
antineutrino is also released.
Neutrinos

Proposed to make beta and positron decay
obey conservation of energy.

These particles possess energy and spin, but
do not possess mass or charge.
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They do not react easily with matter and are
extremely hard to detect.
Gamma Radiation

Gamma photons are released by atoms
which have just undergone a nuclear reaction
when the excited new nucleus drops to its
ground state.

The high energy in a gamma photon is
calculated by E = hf.
Energy in Nuclear Reaction
Mass Energy

Matter is created from energy and can be
converted into energy through nuclear
reactions.

E = mc2

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E – Energy (J)
M – mass (kg)
c – speed of light (3x108m/s)
Energy in Nuclear Reactions
1. Add up the mass (in atomic mass units, u) of the reactants.
2. Add up the mass (in atomic mass units, u) of the products.
3. Find the difference between reactant and product mass. The
missing mass has been converted to energy.
4. Convert mass to kg ( 1 u = 1.66 x 10-27 kg)
5. Use E = mc2 to calculate energy released.
Problem

Complete the reaction, identify the type of
decay, and calculate the energy.
Fission

Fission occurs when an unstable heavy
nucleus splits apart into two lighter nuclei,
forming two new elements.

Fission can be induced by free neutrons.

Mass is destroyed and energy produced
according to E = mc2.
Fusion

Fusion occurs when two light nuclei come together
to form a new nucleus of a new element.

Fusion is the most energetic of all nuclear reactions.
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Energy is produced by fusion in the sun.
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Fusion of light elements can result in nonradioactive waste.