Name
………………………………………
Year 13 Physics
QUANTUM AND NUCLEAR PHYSICS
Quantum and Nuclear Physics
1
Phenomena, Concepts and Principles:




The photoelectric effect;
The electron volt;
Description of the particle/wave duality of light,
The photon;






The Bohr model of the hydrogen atom;
The quantisation of energy;
Discrete atomic energy levels;
Electron transition between energy levels;
Ionisation;
Atomic line spectra (infrared, visible and ultraviolet);


Nuclear binding energy and mass deficit;
Conservation of mass-energy for nuclear reactions.
Relationships:
E  hf
hf    EK
E  mc 2
1
1
1
 R( 2  2 )

S
L
E  eV
v  f
Quantum and Nuclear Physics
En  
hcR
n2
2
QUANTUM PHYSICS
Photo-electric Effect
What has Light got to do with Electricity you might ask? You have seen in a previous topic that light
shows wave properties when travelling. (interference of light.) This idea was commonly accepted prior
to the twentieth century and was explained by classical physics. At the end of the nineteenth century a
phenomena was discovered that the classical wave theory could not successfully explain. This was called
the Photoelectric Effect. This led to the development of the ……………………… Theory. The quantum
theory is the physics of small stuff.
Thermionic Emission: Electrons in a metal are normally bound to it by attractive forces. If an
electron is given enough ……………………………………, it can escape the metal’s surface (c.f a rocket
escaping from earth). This can be done when a metal is …………………………… . The minimum energy
needed for an electron to escape is called the ……………………… ………………………… .
If light is shone on a metal surface, the same thing occurs. Electrons absorb the light energy and gain
sufficient energy to jump out of the metal surface.
Photoelectric Effect
You may see this demonstration.
Light is shone onto an electroscope in different situations. Lead or zinc is placed on the electroscope, the
electroscope is charged positive or negative and light is shone on the metal.
The glass blocks most UV.
glass
Pb
negative
RESULT:
………………………….
Zn
negative
………………………….
Zn
negative
………………………….
Zn
positive
……………………………
In the third one, the leaf swings towards the support, so it must have lost ………………………….
Others show no change.
Quantum and Nuclear Physics
3
The experiment shows that:
(1) light can eject ………………………………. from some metals.
(2) …………………………………… holds its electrons more tightly than ……………………………….………………
(3) …………………… light is needed to knock an electron out of zinc. (Glass stops …………………………light
which has high energy.)
(The minimum energy needed to knock out an electron is called the …………………………
………………………………)
Photoelectric Experiment
AIM: To investigate the emission of electrons from a metal surface by light.
THEORY:
When an electron goes from B to A through the wire, it loses
………………………………… potential energy.
The voltage between A and B is:
energy
charge
E
V
e
B
-
1.5 V
CELL
A
+
voltage 
E
=
exV
“e” is the charge on one electron (-1.6 x 10-19 C)
In a photoelectric cell, light shines on the metal
cathode, causing electrons to be ejected with some
kinetic energy. Some move across to the anode, and
produce a current in the circuit.
Method One:
1.
2.
Connect this circuit (the CRO acts as an
ammeter).
Shine light through an infrared filter onto the
cathode. What happens?
A
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
3.
Increase the infrared light's brightness by bringing it closer. What happens?
………………………………………………………………………………………………………………………………………………………………………
Quantum and Nuclear Physics
4
4.
Shine white light through the red filter onto the cathode. What happens?
………………………………………………………………………………………………………………………………………………………………………
5.
Increase the light's brightness by bringing it closer. What happens?
………………………………………………………………………………………………………………………………………………………………………
7
Now connect the battery as shown below. Increase the opposing voltage. What happens to
the current?
………………………………………………………………………………………………………………………………………………………………………
8.
Explain why.
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
9.
What would you expect to happen if we now
increase the light’s brightness?
…………………………………………………………………………………
…………………………………………………………………………………
……….………………………………………………………………………
…………………………………………………………………………………
A
10.
Increase the brightness, what happens?
…………………………………………………………………………………
…………………………………………………………………………………
Why does the current increase in Method 1 question 5?
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………………………………
Quantum and Nuclear Physics
5
ANALYSIS:
The Classical Theory said light was a continuous wave.
Einstein explained this result by suggesting that light energy was quantised. i.e. the light comes in
little discrete packets of energy called photons. The energy of each packet depending on its
…………………………………...
i.e.
Photon Energy is proportional to …………………………………..
E  hf
The constant (h) is called Planck's Constant.
The Work Function of a metal is the minimum energy needed to remove an electron. Different
metals have different work functions
A photon striking the metal may give its energy to an electron. If this energy is greater than the
work function (energy needed to ………………………… metal), the electron can jump out of the metal and
still have some kinetic energy left over. (The stopping voltage is a measure of this kinetic energy).
i.e.
Electron's kinetic energy =
Energy from Photon - Work Function
E  hf  
compare with
y = mx + c
The threshold frequency is the lowest frequency light that will eject electrons.
The kinetic energy of these ejected electrons is ……………………., so the threshold frequency is…
fT 
The threshold frequency is sometimes called the cut-off frequency.
If you shine light onto a metal, electrons are knocked out, provided the energy of each photon is
bigger than the ………………………… ………………………………… . or if the frequency of each photon is bigger
than the …………………………………….. ……………………………………… .
If the energy of each photon is less than the work function, ……………… electrons are ejected.
The wave theory would predict that if the light was bright enough, electrons will be ejected for
any frequency. This does not happen. If no electrons are ejected by a light beam, the only way
to kick them out is by increasing the ……………………… .
Quantum and Nuclear Physics
6
Einstein explained this using Quantum Theory by saying a beam of light was made up of zillions of
particles called …………………………… . The higher their frequency the more ………………………… they have,
so the easier it is to kick out ………………………… .
Most physicists were opposed to this idea. Robert Millikan carried out experiments for seven years to try
to prove Einstein wrong. We’ll repeat one of them.
Method Two:
We will now test Einstein’s theory and measure the energy of the individual photons of light of
different colours.
If the anode is made negative, the electrons emitted from the cathode are repelled, the current will
be reduced.
If the battery voltage is gradually increased, the anode becomes …………………………. negative and the
current will gradually drop to zero. The maximum kinetic energy of the electrons is proportional to
the stopping voltage
When the current is zero:
EK = Vq (or eV)
(q = charge on electron)
(V = stopping voltage)
Large energies are measured in Joules. Energies at the atomic level are measured in electron
volts.
1 Joule = 6 x 1018 eV
1 eV = ………………………… J
1.
Shine light of different colours (frequencies) onto the cathode. Measure the maximum
energy of the ejected electrons (given by the stopping voltage) for each frequency.
RESULTS:
Colour
2.
(To covert energy in eV to energy in J, multiply by 1.6 x 10-19)
Wavelength
 (nm)
Frequency
f (Hz)
Stopping
Voltage (V)
Electron
Energy (eV)
Electron
Energy (J)
On graph paper, plot a graph of electron energy (E) against light frequency (f) using axis as
shown. Extrapolate the line so it cuts the Energy axis.
Quantum and Nuclear Physics
7
E
f
SUMMARY
•
Low frequency light …………….. knock electrons out of a metal.
•
If you increase the frequency , eventually electrons are ejected.
•
Above this frequency, higher frequency light ejects ………………………….. energy electrons.
•
Increasing the brightness only increases the …………………………….. of photons
Questions:
What is the shape of the graph ?
……………………………………………………………………………………………………………………………………………………………………………………
What is the relationship between the Frequency of light and the Energy of the ejected electrons?
……………………………………………………………………………………………………………………………………………………………………………………
Calculate Planck's Constant (h) from your graph.
……………………………………………………………………………………………………………………………………………………………………………………
Explain the term Work Function.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
Use your graph to determine the value of the work function of the metal cathode.
……………………………………………………………………………………………………………………………………………………………………………………
Explain the term “threshold frequency” or (cut off frequency)
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
Quantum and Nuclear Physics
8
Determine the value of threshold frequency for the metal on the cathode.
……………………………………………………………………………………………………………………………………………………………………………………
On this graph, draw the lines for a metal with:
(a)
(b)
higher work function
lower cut off frequency
E
SUMMARY QUESTIONS
f
1. Describe the process where light ejects electrons from metals.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
2. Describe how the threshold frequency of a metal relates to the work function.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
3. A certain metal has work function of 0.85 eV. What is this in Joules?
……………………………………………………………………………………………………………………………………………………………………………………
4. What is the cut off frequency of this metal?
……………………………………………………………………………………………………………………………………………………………………………………
5. Explain what happens if bright light is shone on the metal, but the frequency is less than
the cut off frequency
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
6. The stopping voltage is increased until the current drops to zero. Explain what happens if
the brightness of the light increases
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
Quantum and Nuclear Physics
9
Analogy:
Imagine a coconut sitting in a metal ring. You want to knock it out by
throwing balls at it. If you throw them slowly, you won’t knock it out,
even if you throw 100 balls one after another. However, one fast ball
will do the trick.
The ball is like a ……………………………………. .
The minimum energy to knock out the coconut is like the …………………… ……………………….
Similarly dim violet light can eject electrons but bright red can’t.
Photoelectric Experiment Review
In the experiment light of various colours was shone
onto the metal cathode. Some colours eject electrons
from the metal surface, they move across to the
anode causing a current in the circuit.
A
To make sure all the electrons ejected from the
cathode reach the anode, a battery can be put in
the
circuit
to
make
the
anode
…………………………………. .
This will cause the current to ……………………………….
up to a limit.
A
We can measure the energy of the electrons
ejected from the cathode (and therefore
the energy of the photons that kicked them
out) by reversing the battery, and increasing
the battery voltage until the current drops
to zero.
A
Quantum and Nuclear Physics
10
By varying the voltage from the battery, the energy of electrons kicked out by different
frequency light can be measured.
Sketch a graph of the results. Label cut off frequency and work function on the graph
Write the equation for the line.
Equation:
Electron
energy
Light
Frequency
Photo Electric Experiment Review
This experiment showed:
1.
The kinetic energy of the ejected electrons is ……………………… to the frequency of the
incoming light.
2.
There is a cut-off ……………………………… for the metal. If the frequency of the light is below
this, electrons are not emitted no matter how bright the light is.
3.
The brightness of the light affects the number of electrons emitted, not their
…………………………………
.
In 1905 Einstein used Planck’s quantum theory to suggest that the light came in individual bundles
or …………………………. of energy called …………………………… .
He said the energy of a single photon depends on its frequency.
(Energy = h x frequency where h is Planck’s Constant)
He explained that the energy of the incoming photon was absorbed by an ………………………… enabling
the electron to escape from the metal.
The energy lost by the electron as it jumps out is called the ………………………… .………………………… .
To knock out an electron, the energy of the photon must be equal to or greater than the …………………
…………………….
So the energy of the ejected electron equals the energy of the incoming …………………………. minus the
…………………………. ………………………… .
Quantum and Nuclear Physics
11
Ek  hf  
i.e.
electron energy = photon energy – work function
(sometimes written as hf = E + B)
Label and explain the diagram
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
1.
A higher frequency photon has more …………………………………… so it gives more energy to the
………………………….…
2.
If the photon energy ( hf ) is less than the…………………………… ………………….……, no electrons are
ejected. Increasing the brightness of the light only increases the …………………………………… of
photons.
i.e Blue photons have …………………………………… frequency than red so have ……………………………………
energy.
light
Dim blue light
……………… …………………… light
……………………… ……………………
ex. If the work function of a metal surface is 3.0 x 10-19 J, this is the minimum ……………………………
energy a photon must have to eject an electron.
A photon with 4.0 x 10-19 J of energy will eject an electron with …………………………………. of kinetic
energy.
Photons with 2.9 x 10-19 J of energy will …………… eject electrons however ……………………………… the
light.
Quantum and Nuclear Physics
12
(nb. photon energies are so small they are usually measured in electron volts (…………)
1J = …………………..eV
1eV = ………………….J
Homework Experiment
Go to the phet simulations website.
Open “Quantum Phenomena”
Open “Photoelectric effect”
Set the battery Voltage to zero.
Shine blue light onto the cathode. Explain what happens.
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
Reduce the frequency to red light. Explain what happens.
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
Measure the cut off wavelength for Sodium metal. Calculate its cut off frequency.
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
Quantum and Nuclear Physics
13
Change the cathode to copper. What happens to the cut off frequency? What does this tell you
about the copper metal?
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
Wave Particle Duality:
Newton said light was made of tiny particles. Later, Thomas Young said light travels in waves,
because light shows diffraction and interference. Einstein reintroduced the idea of particles. He
said light comprises particles (called photons) that have wave properties. This synthesis of the
two concepts is called Wave Particle Duality. We now say that light has wave properties and
particle properties.
Sometimes light behaves like a wave (eg …………………………………………………………………………………………………… )
Sometimes light behaves like a particle (eg ……………………………………………………………………………………………………
)
The energy of each photon is E =
(so it depends on the frequency)
Examples:
ex 1.
The photoelectric effect equation can be written:
½ mv 2  hf  Ø
a. What does each term mean?
b. A certain metal has a work function = 4.8 eV.
Convert this to Joules.
c. Photons with energy 6.0 x 10-19 J are shone on the metal. Calculate their frequency and
wavelength. (Planck’s constant 6.6  10 34 Js )
d. Calculate the energy of the electrons they eject.
e. What is the minimum energy a photon must have to be able to eject an electron from this
metal?
Quantum and Nuclear Physics
14
f. What is the frequency of the lowest energy photon that will eject an electron from this
metal?
Homework Exercise
a
Label the cathode.
A
b.
Light shines onto the cathode and a current flows. Explain why.
c.
The frequency of the light is reduced, and the current goes to zero. Explain why.
d.
The brightness increases but still no current flows. Explain why.
e.
A different cathode is used with the same light and a current flows. Explain why.
f.
A stopping voltage of 0.60V is needed to stop electrons getting across when blue light is
used. Determine the energy of these photoelectrons.
g.
The wavelength of the blue light is 450nm. Calculate the frequency and energy of each
blue photon.
h.
Calculate the work function of the metal surface. Convert this to Joules.
i.
Explain why the glass tube must contain no air.
Quantum and Nuclear Physics
15
Ex 2 The graph shows the energy of photoelectrons as a function of the frequency of incident
light. Label the axis, the cut off frequency, the work function and show how to calculate Planck’s
constant.
Draw the line for a metal with a higher work function
Application
Apart from their use in the development of the quantum theory, the photon tube you
experimented with has many mundane uses. One example is in shop doorways.
A light shines across the doorway onto a photon tube, causing electrons to be ejected and flow
around a circuit. When the light beam is interrupted, the current turns off and this drop in
current activates the buzzer.
Quantum and Nuclear Physics
16
The Hydrogen Spectrum
When atoms are given energy (heating, collisions…) they may emit light.
Eg ………………………………………………………………………………………………………………………………………………………………………….
When the light from an incandescent solid is passed through a diffraction grating, a
…………………………………… spectrum is produced.
When the light from an excited gas is passed through a diffraction grating, a ……………………………………
spectrum is produced. Each element produces a different line spectrum (like a fingerprint).
Hot filament
Diffraction grating
Screen
Excited gas
Hydrogen gas
Hot filament
Quantum and Nuclear Physics
17
A huge amount of information can be obtained by studying the emission and absorbtion spectra of
gases. For example, the composition of distant stars and unknown substances can be determined.
Explain how the element helium was first discovered in the sun
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………
The easiest element to study is hydrogen. The complete series of visible lines for hydrogen gas
looks like
this:
 (nm)
Only the first four lines are visible.
400
500
600
Label the colours of the visible lines.
Many unsuccessful attempts were made to explain the pattern in the lines.
In 1885 Jacob Balmer found a formula that fitted the known wavelengths. Balmer was a
mathematician and had no idea why the lines were in a particular pattern but recognised it as a
series. His formula was developed into:
1 1
 R 2  2 

L 
2
1
R = 1.097 x 107 m-1
(This is Rydberg’s constant)
L = 3,4,5,……………
What is the “L” number for the red line and the violet line? ………………………………………………………
Quantum and Nuclear Physics
18
The series you have observed is called the Balmer series and was the first series of lines
discovered in the hydrogen spectrum because the light was ………………………………………….
Other series were subsequently discovered, and a more general equation was developed:
1 
 1
 R 2  2 

L 
S
1
S is the …………………………..number
L is the …………………………… number
RANGE
S
L
LYMAN
BALMER
PASCHEN
BRACKETT
PFUND
increasing
energy
The sets of series of emission lines look like this: Label the first four series:
increasing
energy
Decreasing ….…………
Increasing ……………………
The Bohr Model.
Balmer had come up with a formula to describe the lines, but physicists wanted to understand the
reason for the lines.
Einstein had applied the …………………………………theory to explain the Photo Electric effect.
Neils Bohr applied the same ideas to explain line spectra.
Ernest Rutherford had already shown that atoms contained a positive ……………………… surrounded by
orbiting ……………………………… .
Bohr suggested that an electron can only orbit in certain allowed energy levels (or quantum
states).
He said if the electron is given ……………………, it can “jump” to a higher energy level. However it is
unstable and falls back down to its original energy level. In doing so, it gives off a photon whose
energy equals the difference between the two …………………………….. levels.
(This “jump” called a quantum leap” is instantaneous and the electron does not exist anywhere in
between)
Quantum and Nuclear Physics
19
High Energy level
(2) electron is unstable,
drops down, loses …………
(1) electron gains …………
(3) …………………… emitted,
Energy = E2 – E1
Low Energy level
Bohr suggested each spectral line was produced by an electron jumping down from a high energy
level to a lower …………………………………… ( a ………………………… leap) producing a …………………………..
There are many energy levels that the electron can exist in.
He further suggested that the different series were produced by quantum leaps ending at
different energy levels.
The Lyman series of lines is produced by electrons dropping to the …………………… state.
The Balmer series of lines is produced by electrons dropping to the …………………………… state.
The Paschen series of lines is produced by electrons dropping to the …………………………… state.
Ionisation
ENERGY 0
(eV)
-.85
-1.51
-3.40
-13.6
The wavelength of the photon emitted by these electron transitions is predicted by Balmer’s
equation.
1 
 1
 R 2  2 

L 
S
1
Quantum and Nuclear Physics
20
S is the …………………………..number
L is the …………………………… number
Combine the above equation with the photon energy equation to derive an equation for the photon
energy in terms of the energy levels.
Hence show that the equation for the electron’s energy in any energy level is:
En  
hcR
n2
n.b The energy levels have negative energy because the electron is assumed to have zero energy
when it it is OUT of the atom. They have less energy IN the atom. And it decreases as they get
closer.
ex. When an electron jumps from a higher energy level to the second energy level it produces the
……………………………… series. The lowest energy transition in the Balmer series produces a photon of
wavelength:
 1 1
 R 2  2 

2 3 
1
(R = 1.097 x 107 m-1)
(a)
Calculate the wavelength of this photon
(b)
Calculate its frequency.
(c)
Calculate its energy.
(d)
Calculate the wavelength of the highest energy photon in the Balmer series.
(e)
Calculate the wavelength of the second lowest energy photon in the Balmer series.
(f)
Calculate the wavelength of the lowest energy photon in the Lyman series.
Quantum and Nuclear Physics
21
Quantum and Nuclear Physics
22
Absorption Lines
Absorption lines are seen when white light shines through a gas. Certain wavelengths don’t pass through
the gas because these photons are absorbed. They have just the right amount of energy to raise an
electron in an atom to a higher energy level. Other photons pass through the atoms because they don’t
have exactly the right energy. The absorption lines are in exactly the same place as the
emission lines.
Homework Questions: Hydrogen Spectrum.
(1)
ENERGY
(eV)
0
-.85
3
2
-1.51
1
-3.40
-13.6
(a)
(b)
(c)
Label the highest and lowest energy electron transitions shown in the Paschen series.
Label four transitions that will produce red, blue, ultraviolet and infrared photons.
Determine the energy needed to ionise an atom if the electron is in the ground state.
(d)
Convert this to Joules
(e)
Calculate the energy of the lowest energy photon in the Lyman series.
(f)
Calculate the frequency of the lowest energy photon in the Lyman series.
(g)
Calculate the wavelength of the lowest energy photon in the Lyman series.
Quantum and Nuclear Physics
23
(h)
Calculate the minimum energy needed to raise an electron from the ground state to the
third quantum state (n=3)
(i)
Determine the energy needed to ionise a hydrogen atom whose electron is in the ground
state.
(j)
Calculate the wavelength of the red photon produced in the Balmer series.
(k)
A photon with an energy of 12.09 eV is absorbed by an electron. The electron then emits
two photons. Calculate the frequency of the lower energy photon
Plasma Globe
Look at the Plasma Globe. Describe how the colour changes as the electrons
move through the globe losing energy.
………………………………………………………………………………………………………………………………………………
Explain why the colour changes.
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
………………………………………………………………………………………………………………………………………………
Glowing Writing
Look at the fluorescent screen after shining violet light onto it. Explain what happens.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
Quantum and Nuclear Physics
24
Repeat with red light. Explain what happens.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
Quantisation of Angular Momentum
Bohr came up with a new idea to explain why certain energy levels or orbits were stable. He
suggested angular momentum was quantised; the size of the quanta was
So any electron had an angular momentum of:
h
2
nh
(n is the ……………………….. number)
2
He did not know why, but it fitted the experimental evidence.
Extension: Matter Waves.
In 1925 a French student, Louis de Broglie had a really bright idea.
”If waves have particle properties (the photoelectric effect) do particles have
wave properties???” i.e. could an electron behave like a wave???
He combined Planck’s Photon equation with Einstein’s Energy equation.
E = hf
hf = mc2
E = mc2
hf
 mc
c
h

p

For large things, (netballs, people cars etc.
 is immeasurably small.
For small things like electrons,  is significant so its wave properties
are noticeable. (a beam of electrons can form an interference
pattern)
h
p
In 1927 Erwin Schrodinger suggested that electrons were
standing waves around the nucleus, and this is why their
energies are quantised. (A standing wave on a guitar string
has only got certain frequencies. They are quantised.)
Summary:
Electrons inhabit certain ………………………… levels or ………………………… ………………………… in an atom.
If they are given energy, they can go up to a ………………………… ………………………… ………………………… .
They are unstable so ………………………… …………………………, giving off a ………………………… .
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The energy of the emitted photon (and therefore its colour) depends on the ………………………… in
…………………………
The wavelength of the emitted photon is given by:
where S means ………………………… and L means ………………………… .
The series of wavelengths represent the electron transitions between …………………………
………………………… .
Homework Questions
ENERGY
(eV)
3
2
1
This diagram shows the Balmer series of lines:
(a)
Label the emission lines 1,2,3 corresponding to the numbered jumps shown in the top
diagram.
(b)
Label the red and UV ends of the Balmer series of emission lines
(c)
Label the emission line containing the highest energy photons.
(d)
Label the emission line containing the longest wavelength photon.
(e)
Label the visible lines.
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NUCLEAR PHYSICS
Ernest Rutherford had shown that atoms comprised a tiny, massive, dense, positive nucleus
surrounded by empty space. In the empty space he supposed that there were electrons. The
question was then asked:
If the nucleus is full of positive charges that ……………………… each other, what holds it all together???
There are only two fundamental forces outside the nucleus…
1)
2)
There are two other fundamental forces that only exist inside the nucleus…
3)
4)
The strong nuclear force is an attractive force that acts between …………………………………… and
overcomes the electrical repulsive force.
(neutrons attract but don’t repel, so they help make larger nuclei stable)
The weak nuclear force is responsible for changes that produce beta decay.
Conservation Principles
In any nuclear reaction the following must be conserved.
Charge
Nucleon number.
Momentum
Mass/Energy
Types of Radioactivity (revision)
With some atoms, especially large ones, the nucleus may be unstable. It may be that the nucleus is too
big, or the combination of protons and neutrons is slightly wrong for that element.
When this happens, the nucleus is likely to undergo …………………………… ……………………… by emitting 
,  or  radiation.
Alpha ( ) Particles
Rutherford collected some of the alpha particles coming from radioactive radon in a glass tube. He
tested the contents of the glass tube and found that it contained helium!
Each  -particle contains two …………………. and two …………………… just the same as a helium nucleus.
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The equation for the reaction is:
226
86
Rn
………………
+
4
2

Note that when we write these equations, the atomic and mass numbers on each side must
balance. This is called conservation of …………………………… number and …………………………………… number.
In alpha decay, the ratio of protons to neutrons is reduced by emission of an alpha particle, making
the Radon more stable
Alpha particles are not very penetrating and are absorbed by several cms of …………. Or several
sheets of ……………… .They travel at up to about 0.1c.
Beta (  ) Particles
 -particles pass easily through paper, but are stopped by a few millimetres of …………………………….
One substance which gives out  -particles is …………………………….
An example of beta decay is:
3
1
H  23He  10 e(   particle )
What has happened inside the nucleus?
One of the neutrons has spontaneously turned into a …………………………… and an …………………………. as
shown below.
1
0
n11 p  10 e
The electron is shot out at high speed (up to about 0.9c).
Gamma (  ) Rays
Gamma rays are the third kind of radiation. They are much more penetrating than  or  particles. It is now known that gamma-rays are identical in character with X-rays, except that
they have a shorter ……………………………. (This makes them more penetrating.) In other words, they
are a photon of ……………………………………………………… radiation. However, gamma rays come from the
nucleus of the atom. Gamma rays usually follow immediately after an  or  decay.
A nucleus often has an energy surplus. It is said to be in an ……………………………… state.
The nucleus immediately drops back down to its stable state by emitting a photon. These photons
are called  -rays.
97
31
Ga*
97
31
Ga
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28
Mass and Energy
This is the moment you’ve been waiting for! We’re going to find out the meaning of ……
E = mc2
This is Einstein’s famous mass energy relationship. It shows that the energy something has is equal
to its mass multiplied by ………………………………………………………………… .
If we could convert all your mass to energy, how much energy would be produced?
(compare this with a large power station that produces about 1016 J a year)
(nb. We are using the word mass to mean inertia, not quantity of matter)
Another way of thinking about it is:
An object’s mass is proportional to its energy. If you compress a spring, its mass increases!!!!!
If you have an alpha particle and wish to pull it apart, a ……………………… is needed to overcome the
strong nuclear force. You have to do ………………………………… on the nucleons. They now have more
energy and so they have more mass. If you measure the mass of the alpha particle and the
separated neutrons and protons, you find the individual neutrons and protons have gained more
mass!!! Weird eh??
This can be explained using the Mass/Energy equation: E = mc2
Mass and energy are equivalent. If something gains energy, its mass …………………………… (and vice
versa.)
(protons and neutrons …………………………… mass when they are pulled out of a Helium nucleus). They
…………………… mass when they form a nucleus because they have ………………… energy in the nucleus.
Extension: So when your chemistry teacher tells you mass is conserved in a chemical reaction, what
they really mean is that the mass does decrease in an exothermic reaction, but the decrease in
mass is negligible.
(ex. Calculate the mass decrease when a burning candle produces 1 000 000 J of heat. )
The missing mass is called the mass deficit and is linked to the energy released by m 
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c2
29
(Extension: Can you see that the decrease in mass is the same as the mass of the energy
released??)
ex1.
The mass of reactants in a reaction is 3.5 x 10-27kg
The mass of products in the reaction is 3.5 x 10-27kg
Calculate the energy released.
(Extension. When we use the term “mass” here, we are meaning “rest mass” because the mass
increases with the speed of the particles)
Binding Energy
The Binding Energy of a nucleus is the energy required to pull the nucleus apart.
n.b the binding energy is NOT the energy the nucleus has.
It’s the energy lost as it forms, so it’s the energy needed to pull it apart.
A more useful measurement is the Binding Energy per Nucleon.
This is the total binding energy divided by the number of nucleons.
The higher the Binding Energy per Nucleon, the …………………………… it is to pull the nucleus apart and
the more …………………………… it is. (Remember this, it’s important!!!)
The higher the binding energy per nucleon,
the less energy each nucleon has, so the less mass it has.
Think of a ball down a well. The deeper the well, the greater the
Binding energy and the ………………… energy it has.
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30
This graph shows that nucleii around the size of Iron 56 have the ……………………………… binding energy
per nucleon. This means they are most …………………………….
Any change from a large nucleus (eg Uranium) splitting (fission) to form smaller nuclei, or small
nuclei (eg Hydrogen) combining (fusion) to form a larger nucleus will result in energy being
……………………………
And the mass of the particles will ……………………………. because the particles are becoming more stable
(less energy).
The reason for this is that the electrical repulsion force is long range. The strong nuclear force is
short range and can only attract nucleons less than about four proton diameters. So as a nucleus
gets bigger, it becomes more stable because there are more nucleons to hold it together.
However when the diameter is about 5 proton diameters, the nucleons at opposite sides no longer
attract but there is still an electric force of repulsion. Nuclei larger than this become less stable
and have a lower binding energy per nucleon.
Fusion
This is the process of joining small nuclei (eg hydrogen) to form larger nuclei (eg Deuterium). The
deuterium has less energy, so it has less mass. The binding energy per nucleon also increases. The
decrease in mass is equivalent to the energy released.
Fusion reactions are responsible for the vast energy output from stars.
ex 1 Explain why fusion can usually only occur at the high temperatures found inside stars
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
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ex 2
Calculate the change in mass when a Helium nucleus is formed from four nucleons.
How much energy is released?
Mass of proton = 1.6726 x 10—27kg
Mass of neutron = 1.6748 x 10—27kg
Mass of He nucleus = 6.6443 x 10—27kg
ex 3:
Deuterium ( H 2 ) and tritium ( H 3 )nuclei may fuse together, as illustrated in the equation below.
2
1
H  13H  24 He  01n
The masses involved in the above reaction are:
mass of deuterium = 3.34250 10–27 kg
mass of tritium = 5.00573 10–27 kg
mass of helium = 6.62609 10–27 kg
mass of neutron = 1.67438 10–27 kg
Speed of light = 3.00 108 m s–1
Charge on the electron = -1.60 10–19 C
(a)
Show that the amount of energy released in the above reaction is 4.30  10 –12 J.
(b)
Explain why energy is released during this reaction.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
(c)
Convert 4.30
10 –12 J into mega electron-volts (MeV).
The reaction described above is one of the possible reactions that occur in the sun. The sun
obtains its radiant energy from a thermonuclear fusion process.
Over its lifetime 1.4 1028 kg of its mass will be converted by the fusion process into radiation
energy.
(d)
The sun radiates at a constant rate of 4.0 1026 Joules per second. Estimate the lifetime
of the sun, assuming that the sun only loses energy by radiation.
____
lifetime =
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Fission
Spontaneous Fission is when a nucleus just breaks apart. A nucleus can also be caused to split or
……………………………. In 1930, scientists started shooting neutrons at the nuclei of heavy metals. All
sorts of things happened. They made new elements that were heavier than uranium. They made old
elements radioactive. In 1939, a chemist named Otto Hahn was shooting neutrons into uranium. When
he looked at the result, he found a little barium mixed up with the uranium. It had not been there
before, and it could only have come from the …………………………….
A slow-moving neutron penetrates the
235
92
U
nucleus. The nucleus wobbles like jelly, then
…………………………… into two large pieces. The two pieces are sometimes (but not always) barium and
krypton. As well as the two large pieces, some extra ……………………………fly out at high speed.
141
56
Ba
235
92
U
92
36
Kr
Slow neutron
Write the reaction equation
The reaction releases ……………………………. This is why the neutrons come out fast. This reaction is
called fission (which means ……………………………), and we say that uranium-235 is fissile (it can be split
by low-energy neutrons).
ex1. Calculate the energy released (in Joules.)
U-235 : 390.2480 x 10-27 kg
Kr-92 : 152.5794 x 10-27 kg
Ba-141 : 233.9616 x 10-27 kg
n
: 1.6747 x 10-27 kg
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How much energy can be released by a fuel rod containing 5 x 1020 U235 nucleii?
Nb, because the energy of each reaction is very small, energies are often quoted in
electron volts (or eV). One eV = 1.6 x 10-19 J.
Convert the above energy to electron Volts.
ex 2
Physicists are currently working towards building fusion reactors. Explain their advantages
compared with conventional fission reactors.
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
ex 3. Suppose we start with just 1 kg of U-235 in a nuclear reactor. (It would be a block the size
of a 50 gram Mars Bar). After the fission reactions are complete, there is still 999 grams of
material left.
Calculate the energy of the missing gram . (This is sometimes called the …………. ……………..)
………… joules
……………eV
This is about the same amount of energy as there is in 3 million litres of LPG
(When 1.0 kg of coal burns, its mass decreases by about 0.0001 g.)
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Pair Production (extension)
It used to be thought that matter was indestructible and couldn’t be created or destroyed.
Physicists have however found that matter can be converted into radiation and vice versa.
………………
………………
………………
Experiments have shown that when a high energy gamma photon smacks into a massive nucleus, it
can lose all its energy. This energy is used to create two particles, an electron and a
………………………………. (This is called anti-matter). The energy of the photon is equivalent to the mass
of the particles. Note that all the conservation laws still apply.
ex 1. Calculate the minimum energy the photon must have to create the pair.
(me= 9.1 x 10-31 kg)
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The reverse also occurs. Label the diagram. Describe what happens in this case
………………
………………
………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………………………
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These energy diagrams may help show how mass can decrease and energy can be
released during fission and fusion.
Fusion is the joining of two small nucleii to make a larger one.
fusion
fission
The Potential Energy is less, (BEPN increases)
so Energy is released, and its mass decreases.
m
E
c2
The energy barrier is due to the electrical
repulsive forces between the positive nuclei.
ENERGY
The well is due to the strong nuclear force (attraction)
Fission is the splitting of a large nucleus to make two small nucleii.
The Potential Energy is less, (BEPN increases)so Energy is released, and its mass decreases.
m
E
c2
The energy barrier is due to the attraction of the
strong nuclear force between the nucleons.
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Nuclear Physics
SUMMARY
Complete nuclear equations with charge and nucleon numbers.
eg.
14
7
N  ZAX 146C  11H
Know the symbols for: Alpha, beta, gamma and neutron.
Know that during fusion, small nuclei fuse to make bigger ones. (BEPN increases) The initial mass is
bigger than the final mass.
Mass decreases, energy is given out.
Know that during fission, a big nucleus splits to make smaller ones. (BEPN increases) . The initial
mass is bigger than the final mass. Mass decreases, energy is given out.
The missing mass is called mass deficit and is converted to energy
The energy released is given by E =
BE per nucleon
Atomic no
The binding energy is the energy needed to pull the nucleons from the nucleus
This graph shows BE per nucleon peaks at iron. Iron is most stable because it has the most binding
energy per nucleon and requires the most energy to separate
Because iron has the greatest binding energy per nucleon this means that the rest mass of an iron
nucleus is much less than the rest mass of its individual nucleons. Hence, iron will have the least
average mass per nucleon when compared to other elements.
Convert eV to J and back.
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