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## Quantum and Nuclear Physics

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Title: Quantum and Nuclear Physics

1
Quantum and Nuclear Physics
The Photoelectric effect
2
Waves or Particles?
3
The Photoelectric effect
4
How are the electrons released?
Powerful red laser
No electrons released
5
Photoelectron Energy
Photon
Photon Energy work function kinetic energy of
electron
6
Determining Plancks constant
• Add different filters under the light source

7
Photoelectric experiment
• Take measurements of stopping potential and
wavelength to determine Plancks constant and the
threshold frequency

Plot a graph of stopping potential versus
frequency
8
Photoelectric Effect Vstop vs. Frequency
hfmin
Slope h Plancks constant
-f
9
Determining h from the graph
10
Photoelectric Effect IV Curve Dependence
Intensity I dependence
Vstop Constant
f1 gt f2 gt f3
Frequency f dependence
f1
f2
f3
Vstop? f
11
Is light a wave or a particle?
• http//www.schoolphysics.co.uk/age16-19/Quantum20
physics/text/Photoelectric_effect_animation/index.
html

F
E max
V Stopping voltage
12
• 1. The work function for lithium is 4.6 x 10-19
J.
• (a) Calculate the lowest frequency of light that
will cause photoelectric emission. (6.9 x 1014 Hz
)
• (b) What is the maximum energy of the electrons
emitted when light of 7.3 x 1014 Hz is used?
(0.24 x 10-19 J )
• 2. A frequency of 2.4 x 1015 Hz is used on
magnesium with work function of 3.7 eV.
• (a) What is energy transferred by each photon?
• (b) Calculate the maximum KE of the ejected
electrons.
• (c) The maximum speed of the electrons.
• The stopping potential for the electrons.
• (a) 1.6 x 10-18 J
• (b) 1.0x 10-18 J
• (c) v 1.5 x 106 m s-1
• (d) Vs 6.3 V

13
Questions
• Tsokos page 396 qs 1-7.

14
Review of Bohr and deBroglie
• Background
• Balmer found equation for Hydrogen spectrum but
didnt know what it meant.
• Rutherford found that atoms had a nucleus, but
didnt know why electrons didnt spiral in.
• Bohr postulates quantized energy levels for no
good reason, and predicts Balmers equation.
• deBroglie postulates that electrons are waves,
and predicts Bohrs quantized energy levels.
• Note no experimental difference between Bohr
model and deBroglie model, but deBroglie is a lot
more satisfying.

15
Davisson and Germer -- VERY clean nickel
crystal. Interference is electron scattering off
Ni atoms.
e
e det.
e
e
e
e
scatter off atoms
e
e
e
e
e
e
move detector around, see what angle electrons
coming off
Ni
16
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17
e
e
e
e
e
e det.
e
Observe pattern of scattering electrons off
atoms Looks like . Wave!
e
e
Ni
18
Electron diffraction
Diffraction rings
19
Calculating the De Broglie ?
? h/p ( h/(2Ekm)1/2 ) h
Plancks constant p Momentum

In 1923, French Prince Louis de Broglie,
generalised Einstein's work from the specific
case of light to cover all other types of
particles. This work was presented in his
doctoral thesis when he was 31. His thesis was
greeted with consternation by his examining
in advance and vouched for de Broglie. He passed!
20
de Broglie questions
• Calculate the wavelengths of the deBroglie
waves associated with
• a)a 1kg mass moving at 50ms-1
• b)an electron which has been accelerated by a
p.d. of 500V.

21
a)Discuss briefly deBroglies hypothesis and
mention one experiment which gives evidence to
support it. b)Calculate the wavelength of the
deBroglie wave associated with an electron in
the lowest energy Bohr orbit. (The radius of the
lowest energy orbit according to the Bohr theory
is 5310-11m.)
22
Questions
• Tsokos page 396 qs 8-10

23
History of Quantum Mechanics
Max Planck's work on the 'Black Body' problem
started the quantum revolution in 1900. He showed
that energy cannot take any value but is arranged
in discrete lumps later called photons by
Einstein. In 1913, Niels Bohr proposed a model
of the atom with quantised electron orbits.
Although a great step forward, quantum physics
was still in its infancy and was not yet a
consistent theory. It was more like a collection
of classical theories with quantum ideas applied.
Starting in 1925 a true 'quantum mechanics' a
set of mathematically and conceptual 'tools'
was born. At first, three different incantations
of the same theory were proposed independently
and were then shown to be consistent. Quantum
mechanics reached its final form (essentially
unchanged from today) in 1928.
24
Participants of the 5th Solvay Congress,
Brussels, October 1927
W. Heisenberg
W. Pauli
E. Schrödinger
N. Bohr
A. Einstein
M. Planck
L.V. de Broglie
M Curie
25
Models of the Atom
• Thomson Plum Pudding
• Why? Known that negative charges can be removed
from atom.
• Problem just a random guess
• Rutherford Solar System
• Why? Scattering showed hard core.
• Problem electrons should spiral into nucleus in
10-11 sec.
• Bohr fixed energy levels
• Why? Explains spectral lines.
• Problem No reason for fixed energy levels
• deBroglie electron standing waves
• Why? Explains fixed energy levels
• Problem still only works for Hydrogen.
• Schrodinger will save the day!!

26
Different view of atoms
The Bohr Atom
Electrons are only allowed to have discrete
energy values and these correspond to changes in
orbit.
The Schrodinger Atom
Electrons behave like stationary waves. Only
certain types of wave fit the atom, and these
correspond to fixed energy states. The square of
the amplitude gives the probability of finding
the electron at that point
27
Spectra
Consider a ball in a hole
When the ball is here it has its lowest
gravitational potential energy.
We can give it potential energy by lifting it up
If it falls down again it will lose this gpe
28
Spectra
A similar thing happens to electrons. We can
excite them and raise their energy level
29
Spectra
If we illuminate the atom we can excite the
electron
Light
Energy change 3.4eV 5.44x10-19J.
Using Ehc/? wavelength 3.66x10-7m
(In other words, ultra violet light)
30
Example questions
1. State the ionisation energy of this atom in eV.
2. Calculate this ionisation energy in joules.
3. Calculate the wavelength of light needed to
ionise the atom.
4. An electron falls from the -1.5eV to the -3.4eV
level. What wavelength of light does it emit and
what is the colour?
5. Light of frequency 1x1014Hz is incident upon the
atom. Will it be able to ionise the atom?

31
Spectra
32
Emission Spectra
33
Observing the Spectra
Microscope (to observe the spectrum)
Light source
Collimator
Gas
Diffraction grating (to separate the colours)
34
Questions
• Tsokos page 405 qs 1-7.

35
Models of the Atom
• Thomson Plum Pudding
• Why? Known that negative charges can be removed
from atom.
• Problem just a random guess
• Rutherford Solar System
• Why? Scattering showed hard core.
• Problem electrons should spiral into nucleus in
10-11 sec.
• Bohr fixed energy levels
• Why? Explains spectral lines.
• Problem No reason for fixed energy levels
• deBroglie electron standing waves
• Why? Explains fixed energy levels
• Problem still only works for Hydrogen.
• Schrodinger will save the day!!

36
Schrödinger model
Schrödinger set out to develop an alternate
formulation of quantum mechanics based on matter
waves, à la de Broglie. At 36, he was somewhat
older than his contemporaries but still succeeded
in deriving the now famous 'Schrödinger Wave
Equation.' The solution of the equation is known
as a wave function and describes the behavior of
a quantum mechanical object, like an electron. At
first, it was unclear what the wave function
actually represented. How was the wave function
related to the electron? At first, Schrödinger
said that the wave function represented a 'shadow
wave' which somehow described the position of the
electron. Then he changed his mind and said that
it described the electric charge density of the
electron. He struggled to interpret his new work
until Max Born came to his rescue and suggested
that the wave function represented a probability
more precisely, the square of the absolute
magnitude of the wavefunction is proportional to
the probability that the electron appears in a
particular position. So, Schrödinger's theory
gave no exact answers just the chance for
something to happen. Even identical measurements
on the same system would not necessarily yield
the same results! Born's key role in deciphering
the meaning of the theory won him the Nobel Prize
in Physics in 1954.
37
Quantum Mechanical tunneling
In the classical world the positively charged
alpha particle needs enough energy to overcome
the positive potential barrier which originates
from protons in the nucleus. In the quantum world
an alpha particle with less energy can tunnel
through the potential barrier and escape the
nucleus.
38
Electron in a box model
Electrons will form standing waves of wavelength
2L/n
39
Kinetic Energy of an electron in a box
• When the momentum expression for the particle in
a box
• is used to calculate the energy associated with
the particle

40
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41
Heisenberg uncertainty principle
Heisenberg made one fundamental and long-lasting
contribution to the quantum world the
uncertainty principle. He showed that quantum
mechanics implied that there was a fundamental
limitation on the accuracy to which pairs of
variables, such as (position and momentum) and
(energy and time) could be determined. If a
'large' object with a mass of, say, 1g has its
position measured to an accuracy of 1 , then the
uncertainty on the object's velocity is a minute
10-25 m/s. The uncertainty principle simply does
not concern us in everyday life. In the quantum
world the story is completely different. If we
try to localize an electron within an atom of
diameter 10-10 m the resulting uncertainty on its
velocity is 106 m/s!
42
Heisenberg uncertainty principle
43
Nuclear physics
44
Determining the size of the nucleus
45
• Make an arithmetical check to show that at
distance r 1.0x1014 m, the electrical
potential energy, is between 20 MeV and 25 MeV,
as shown by the graph.
• 2.How does the electrical potential energy change
if the distance r is doubled?
• 3.From the graph, at what distance r, will an
alpha particle with initial kinetic energy 5 MeV
colliding head-on with the nucleus, come to rest
momentarily?

46
1. Substituting values gives
2. Halves, because the potential energy is
proportional to 1/r. 3. About 4.6x1014 m, where
the graph reaches 5 MeV.
47
Circular paths
Recall
2 protons, 2 neutrons, therefore charge 2
1 electron, therefore charge -1
-
Because of this charge, they will be deflected by
magnetic fields
-
These paths are circular, so Bqv mv2/r, or
48
Bainbridge mass spectrometer
Ions are formed at D and pass through the cathode
C and then through a slit S1
A particle with a charge q and velocity v will
only pass through the next slit S2 if the
resultant force on it is zero that is it is
traveling in a straight line. That is if
Therefore
In the region of the Mag field
r Mv/(Bq)
Bqv Mv2/r
Therefore
49
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50
Nuclear energy levels
There are 2 distinct length of tracks in this
Alpha decay Therefore, the energy levels in the
nucleus are discrete
51
The existence of Neutrinos
How can a 2 body system create a spectrum of
energies?
There must be a 3rd particle
The Neutrino was postulated
A 3 body system has many solutions
A 2 body system only has one solution
52
Changes in Mass and Proton Number
Beta - decay
Beta decay
53
dN/N -?dt which when integrated, gives
Taking antilogs of both sides gives
54
Half life and the radioactive decay constant
When N No/2 the number of radioactive nuclei
will have halved
Therefore when t T1/2 N No/2 Noe-?T1/2
and so 1/2 e-?T1/2 . Taking the inverse gives
2 e?T1/2 and so
55
Measuring long half lives
• If the half life is very long, then the activity
(A) is constant
• Analysis of a decay curve cannot give the half
life.
• If the mass of the substance is measured, then
• A -?N, so a measurement of the activity enables
Measuring long half lives to be calculated (N
from mass).
• T1/2 can be calculated from ?.

56
Measuring short half lives
• Each decay can cause an ionisation
• This can generate an electric current
• If the current is displayed on an oscilloscope,
then
• The limit is the response time of the
oscilloscope (typically µs).

57
Questions
• Tsokos page 412 qs 1-20