Name……………….
Class……….
Plymstock School Physics
Department
Module G485.3
Nuclear Physics
student booklet
Lesson 33 notes - The Nuclear Atom
Objectives
(a) describe qualitatively the alpha-particle scattering experiment and the
evidence this provides for the existence, charge and small size of the nucleus
(HSW 1, 4c);
(b) describe the basic atomic structure of the atom and the relative sizes of
the atom and the nucleus;
Outcomes
Be able to describe what makes up an atom and recall the relative sizes of the
atom and the nucleus.
Be able to describe qualitatively the alpha-particle scattering experiment.
Be able to describe the observations made from this experiment.
Be able to explain how these observations are evidence for the existence,
charge and small.
Rutherford Scattering
Rutherford alpha particle scattering experiment
lead block to select
narrow beam of alpha
particles
radium source of
alpha particles
thin gold
foil
scattered alpha
particles
alpha particle
beam
microscope to view zinc
sulphide screen, and count
alpha particles
vary angle of
scattering
observed
zinc sulphide screen,
tiny dots of light where
struck by alpha particle
The experiment takes place in a vacuum to avoid problems of absorption by
air.
Alpha particles are shot at the Gold Leaf. Some were deflected, some
rebounded (1 in 10000). This led to the explanation that the gold leaf was
made up of very small particles that had the majority of there charge and
mass concentrated in a very small space at the centre of the particle: The
nucleus.
The Atom
We now think of atoms in terms of a positively charged nucleus with negative
electrons orbiting it. In the Bohr atom these electron shells (energy levels) are
just the most likely place that an electron will be found and explained using
Quantum Theory.
Atomic Sizes
•Electron size ~ 10-18 m
•Nucleus sizes ~ 1 fm
•Atomic sizes ~ 1Å
•Hydrogen molecule length ~ 1.28Å
•Water Molecule size ~ 2.8Å
Lesson 33 questions – The Atom
1.
Describe briefly the two conflicting theories of the structure of the atom.
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2.
Why was the nuclear model of Rutherford accepted as correct?
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3.
What would have happened if neutrons had been used in Rutherford’s experiment?
Explain your answer.
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4.
What would have happened if aluminium had been used instead of gold in the alpha
scattering experiment? Explain your answer.
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5.
What three properties of the nucleus can be deduced from the Rutherford scattering
experiment? Explain your answer.
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6
Describe briefly one scattering experiment to investigate the size of the
nucleus of the atom.
Include a description of the properties of the incident radiation which
makes it suitable for this experiment.
In your answer, you should make clear how evidence for the size of the
nucleus follows from your description.
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[Total 8 marks]
Lesson 34 – The Strong Nuclear Force
Objectives
(c) select and use Coulomb’s law to determine the force of repulsion, and
Newton’s law of gravitation to determine the force of attraction, between two
protons at nuclear separations and hence the need for a short range,
attractive force between nucleons (HSW 1, 2, 4);
(d) describe how the strong nuclear force between nucleons is attractive and
very short-ranged;
Outcomes
Be able to describe why there is a need for the short range attractive force
between nucleons.
Be able to use Coulomb’s Law and Newton’s Law of gravitation to be able to
calculate forces within nuclei to explain why there is a need for the short
range attractive force between nucleons.
Be able to describe the properties of th strong nuclear force.
Be able to interpret graphical representations of the strong nuclear force.
Gravitation and Electrostatic forces
Imagine 2 particles with a charge +e (e.g. 2 protons).
Gravity will pull them together (gravity is an attractive force).
Since they have the same charge Coulomb’s electrostatic force will push them
apart (a repulsive force).
r
+
+
Calculate the Gravitational force and Electrostatic force between them:
•Data
•p = 1.602x10-19C
•ε0 = 8.85x10-12Fm-1
•mp = 1.673x10-27kg
•G = 6.673x10-11Nm2
•r = 1fm
You should find that the ratio between the forces Fe:Fg is 1.2x1036
In other words it’s not gravity that’s holding nuclei together; its contribution is
negligible – there must be another force
– A NUCLEAR FORCE.
The Strong Nuclear Force
Characteristics:
I.
It is an attractive force between nucleons - We have discovered this
from our calculations of the Coulomb force.
II.
It is repulsive at very short range - If it were not then all nucleons
without a charge would be able to pull each other into an infinitesimally small
point. – This does not happen.
III.
It does not extend beyond distances of a few femtometres Evidence from the Rutherford Scattering experiment shows that alpha
particles describe paths explained by Coulomb repulsion until thy get very
close to the nucleus whereby explanations need an extra force – the Strong
Force – to describe their paths.
IV.
It does not depend on the charge of the nucleons - both neutrons
and protons feel the strong force – the evidence for this again comes from
scattering experiments.
V.
It is readily saturated by surrounding nucleons - The strong force is
stronger than the electrostatic force, but acts over a shorter distance. Adding
more nucleons is favoured with small nuclei but not with large. e.g. adding a
proton to a small vs. large nucleus.
Force vs Seperaration
The graph shows how the Force between
2 nucleons varies with the separation
between the nuclei.
Lesson 34 questions – Nuclear Forces
1.
Fig. 1 shows two protons A and B in contact and at equilibrium inside a
nucleus.
A
B
Fig. 1
Proton A exerts three forces on proton B. These are an electrostatic force
FE, a gravitational force FG and a strong force FS.
(a)
On Fig. 1, mark and label the three forces acting on proton B.
Assume that every force acts at the centre of the proton.
[2]
(b)
Write an equation relating FE, FG and FS.
[1]
(c)
The radius of a proton is 1.40 × 10–15 m.
Calculate the values of
(i)
FE
FE = ..................................... N
[2]
(ii)
FG
FG = ..................................... N
[2]
(iii)
FS.
FS = ..................................... N
[1]
(d)
Comment on the relative magnitudes of FE and FG.
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[1]
(e)
Fig. 2 shows two neutrons in contact and at equilibrium inside a
nucleus.
Fig. 2
Without further calculation, state the values of FE, FG and FS for
these neutrons.
(i)
FE = .................................................................................. N
[1]
(ii)
FG = .................................................................................. N
[1]
(iii)
FS = ................................................................................. N
[1]
[Total 12 marks]
2.
This question is about the strong and electrostatic forces inside a
nucleus.
The figure below shows how the strong force (strong interaction) and the
electrostatic force between two protons vary with distance between the
centres of the protons.
strong
force
force
electrostatic
force
0
(a)
0
distance
between centres
Label on the figure the regions of the force axis which represent
attraction and repulsion respectively.
[1]
(b)
(i)
On the figure above, mark a point which represents the
distance between the centres of two adjacent neutrons in a
nucleus. Label this point N.
Explain why you chose point N.
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(ii)
On the figure, mark a point P which represents the distance
between two adjacent protons in a nucleus.
Explain why you chose point P.
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[2]
(c)
On the figure, sketch a line to show how the resultant force
between two protons varies with the distance between their
centres. Pay particular attention to the points at which this line
crosses any other line.
[3]
(d)
(i)
Write an expression for the electrostatic force between two
point charges Q which are situated at a distance x apart.
[1]
(ii)
The electrostatic force between two protons in contact in a
nucleus is 25 N.
Calculate the distance between the centres of the two
protons.
distance = ...................................... m
[2]
[Total 11 marks]
Lesson 35 notes – Nuclear Properties
Objectives
(e) estimate the density of nuclear matter;
(f) define proton and nucleon number;
(g) state and use the notation AZX for the representation of nuclides;
(h) define and use the term isotopes;
Outcomes
Be able to define proton and nucleon number.
Be able to define and use the term isotope.
Be able to state and use the notation AZX for the representation of nuclides.
Be able to estimate the density of nuclear matter.
Nuclide notation
A is also the total number of nucleons – The Nucleon Number.
Isotopes
We can use the isotopes of carbon as an example of this notation. All
elements with the same number of protons have near identical chemical
properties. An Isotope has the same number of protons but different numbers
of neutrons. i.e. The same proton number (Z) but different nucleon number
(A). Isotopes generally have different nuclear stability, (the ability to stick
around)
In the example of Carbon, the element is determined by the atomic number 6.
Carbon-12 is the common isotope, with carbon-13 as another stable isotope
which makes up about 1%. Carbon 14 is radioactive and the basis for carbon
dating.
The Nuclear Radius
You may expect that (and it can be proven that) the volume V of the nucleus
is proportional to of the number of nucleons A. V is also proportional to the
cube root of the radius r, so it follows that A is directly proportional to r3. Or
r = r0A1/3
where r0 is the radius of one nucleon.
Nuclear Density
It can be show that ρ=3m/(4r03) where ρ is the nuclear density (the density of
any nuclide) and r0 is the radius of a nucleon.
ρ=1017kgm-3
This is the same for more or less all atoms with a few exceptions. Which is
very dense. These densities are similar to those of neutron stars.
Lesson 35 questions – Nuclear Properties
A periodic table may be needed
A
1 Write down the nuclear notation ( Z X ) for:
(a)
an alpha particle
(1)
(b)
a proton
(1)
(c)
a hydrogen nucleus
(1)
(d)
a neutron
(1)
(e)
a beta particle
(1)
(f)
a positron.
(1)
A
2 Write down the nuclear notation ( Z X ) for
(a)
carbon 13
(1)
(b)
nitrogen 14
(1)
(c)
neon 22
(1)
(d)
tin 118
(1)
(e)
iron 54
(1)
3
Explain what is meant by the statement that the strong interaction is a
short-range force and explain what this implies about the densities of nuclei of
various sizes.
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[Total 3 marks]
Lesson 36 – Nuclear Reactions
Objectives
(i) use nuclear decay equations to represent simple nuclear reactions;
(j) state the quantities conserved in a nuclear decay.
Outcomes
Be able to describe that heaver elements are more radioactive.
Be able to use nuclear decay equations to represent simple nuclear reactions.
Be able to state the quantities conserved in a nuclear decay.
Be able to explain why heaver elements are more radioactive.
N-Z plot (Segrè plot).
Neutron
number
/N
n
p + - + 
A
+
p
B
n + + + 
Proton number
/Z
The graph shows Neutron Number against Proton number and you can see
that in heavier elements the number of neutrons is bigger than the number of
protons. This can be explained with an understanding of the forces inside a
nucleus. But as these numbers become more and more unbalanced the
nucleus becomes more and more unstable until they break down
radioactively.
The grids below show some of the emissions given by unstable nuclei:
Grid showing change in A and Z with different emissions
Worked examples:
A, Z-1
Nucleon number
A, Z
A, Z+1
(A)
-
+

A-4, Z-2
Proton number (Z)
Neutron number
(N)
+
N+1, Z-1
N, Z
-
N-2, Z-2
N-1, Z+1

Proton number (Z)
Equations for alpha, beta and gamma decay
Nuclear decay processes can be represented by nuclear equations. The word
equation implies that the two sides of the equation must ‘balance’ in some
way.
Examples of equations for the sources used in school and college labs.
 sources are americium-241,
241
95
Am
237
4
Am

Np

He
.
93
2
241
95
- sources are strontium-90,
90
38
Sr
90
0
Sr

Np

e
.
39
1
90
38
(Extension
The underlying process is:
n –> p + e- + 
Here,  is an antineutrino.
You can translate n –> p + e- into the AZ notation:
1
n
0
.)
1H
1e
1
0
60
 sources are cobalt-60 27 Co . The  radiation comes from the radioactive
60
60
60
daughter 28 Ni of the  decay of the 27 Co . The 28 Ni is formed in an ‘excited
state’ and so almost immediately loses the energy by emitting a  ray. They
are only emitted after an  or  decay, and all such  rays have a well-defined
energy. (So a cobalt-60 source, which is a pure gamma emitter, must be
designed so that betas are not emitted. How? – (by encasing in metal which is
thick enough to absorb the betas but which still allows gammas to escape.)
Decay processes
R a d io a c t iv e d e c a y p r o c e s s e s
 decay
Z
N
Z–2
N –2
p r o to n n u m b e r Z

2 fe w e r p r o to n s
2 fe w e r n e u tr o n s
– decay
–
Z
N
Z+1
N–1

p r o to n n u m b e r Z
1 m o r e p r o to n
1 le s s n e u tr o n
+ decay
+
Z–1
N+1

Z
N
p r o to n n u m b e r Z
1 le s s p r o to n
1 m o r e n e u tr o n
 d e c a y
Z
N
p r o to n n u m b e r Z

s a m e p r o to n s
a n d n e u tr o n s
Summary of Nuclear Decay
For nuclear decay to occur the mass of the daughter nuclei must be less than the
parent. In radioactive decay, A, Z and N are all conserved as is the number of
particles. We get neutrinos and antineutrinos in some decay because of this. The mass
that is lost is given as energy by the equation E=mc2. (more on this later!)
Lesson 36 background notes – history of radioactivity
Wilhelm Conrad Roentgen (1845-1923)
On November 8th 1895 Roentgen
discovered X-Rays. A selfless man and a
very great investigative scientist, he had
noticed the X-rays penetrating an opaque
paper around a cathode ray tube to make a
fluorescent screen glow.
Antoine Henri Becquerel (1852-1908)
Henri Becquerel came from a scientific
background and once he heard of Roentgen’s
discovery began his own on fluorescent
materials. At first he thought that the Uranium
crystals absorbed the Sun’s light and reradiated
X-rays out, but he soon found that this was not
the case. Uranium was spontaneously emitting
another type of radiation.
Becquerel experimented with the radiation and
found that although similar to X-rays, the
radiation could be deflected by magnets and so
must contain negatively charged particles.
Pierre Curie (1859-1906)
Marie Curie (1867-1934)
After they married in 1895, Pierre and
Marie Curie researched the phenomenon
of radioactivity together (although Henri
Becquerel discovered it, it was Marie
who coined the phrase “Radioactivity”).
They researched a uranium ore called
pitchblende and found that after
extraction of pure uranium it was less
active then when in the ore. This led her
to the discoveries of polonium and
radium.
Pierre died in a road accident in 1906 and Marie was awarded his teaching
post. She died in 1934 from pernicious anaemia; probably caused by
overexposure to nuclear radiation.
Ernest Rutherford (1871-1937)
The Grandfather of Nuclear physics made
some amazing discoveries about the
changes in radioactive particles that occur.
He also is the man that pretty much
described the atom as we think of it today.
He was experimenting by firing alpha
particles at a gold leaf when he noticed that 1
in 8000 of the particles bounced off it instead
of going through. He surmised that this was due to most of the mass of an
atom being concentrated in one place with nothing much around it apart from
electrons at a great (atomically speaking) distance.
The amazed Rutherford commented that it was "as if you fired a 15-inch naval
shell at a piece of tissue paper and the shell came right back and hit you."
Lesson 37 notes – Quarks
Objectives
(a) explain that since protons and neutrons contain charged constituents
called quarks they are, therefore, not fundamental particles;
(b) describe a simple quark model of hadrons in terms of up, down and
strange quarks and their respective antiquarks, taking into account their
charge, baryon number and strangeness;
(c) describe how the quark model may be extended to include the properties
of charm, topness and bottomness;
(d) describe the properties of neutrons and protons in terms of a simple quark
model;
Outcomes
Be able to explain that since protons and neutrons contain charged
constituents called quarks they are, therefore, not fundamental particles.
Be able to describe a simple quark model of hadrons in terms of up, down and
strange quarks and their respective antiquarks, taking into account their
charge, baryon number and strangeness.
Be able to describe the properties of neutrons and protons in terms of a
simple quark model.
Be able to describe how the quark model may be extended to include the
properties of charm, topness and bottomness.
What’s stuff made of?
Just over 100 years ago we’d find out about radioactive particles and had
started discovering what stuff
was actually made of. The
Greeks had come up with the
idea of an indivisibly small
atom that makes up
everything. This was not quite
right when we found out that
inside atoms were nuclei, and
inside these were nucleons
(protons and neutrons) and
around these were electrons.
Theoretical physicists came
up with the idea of Quarks in
order to explain what
electrons and other cosmic
particles were made from.
With the use of particle
accelerators these Quarks
were proven to exist and
many exotic fundamental
particles left their trails.
Fundamental Particles
The diagram shows the different classes of fundamental particles. There are 3
types of fundamental particle: Bosons, Leptons and Quarks. On the diagram;
Mesons and below are made up of Quarks.
Flavours
Bosons
There are 6 types or “flavours” of Quarks each with different properties as
shown in the table:
Quark (Flavour) Symbol Spin Charge
Up
U
1/2
+2/3
Baryon
S
Number
1/3
0
C
B
T
0
0
0
Down
D
1/2
-1/3
1/3
0 0 0 0
Charm
C
1/2
+2/3
1/3
0 +1 0 0
Strange
S
1/2
-1/3
1/3
-1 0 0 0
Top
T
1/2
+2/3
1/3
0 0 0 +1
Bottom
B
1/2
-1/3
1/3
0 0 -1 0
S – Strangeness, C – Charm, B – Bottomness, T – Topness
On top of this each individual Quark of the same flavour can have a different
colour that represent forces.
There are also corresponding Anti-Particle pairs for each of these Quarks.
Ant-Particles will be discussed in the next lesson.
Baryons, Mesons and Leptons
The Quark Model says that different combinations of different flavoured
quarks make up all other particles.
So a Proton is made up of 2 ups and a down since that makes a charge of +1.
And a neutrons is made of 2 downs and an up since that makes a charge of
zero.
Neutrons and Protons are both heavy Baryons since they are made of 3
quarks.
Mesons are made up of a quarks and an antiquarks and are the medium
sized particles.
Both mesons and baryons interact via the strong nuclear force.
Leptons are a class of their own and another fundamental particle. They are
some of the smallest particles like electrons. They have a charge of +/-1 and
vary in mass and “size”.
Extension: The Standard Model
Leptons and Quarks are fundamental particles associated with matter and are
made up of Quarks and Leptons. Bosons are also fundamental particles that
are mostly associated with forces.
Timeline of fundamental particles discoveries:
http://en.wikipedia.org/wiki/Timeline_of_particle_discoveries
Lesson 37 questions – Quarks
Name…………………
(
/23)…….%…….
MOST
1.
(i)
State the quark composition of the neutron.
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[1]
(ii)
Complete the table to show the charge Q, baryon number B and
strangeness S for the quarks in the neutron.
quark
Q
B
S
[2]
(iii)
Hence deduce the values of Q, B and S for the neutron.
Q …………… B …………… S ……………
[1]
[Total 4 marks]
2.
(i)
Name the group of particles of which the electron and the positron
are members.
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[1]
(ii)
Name another member of this group.
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[1]
[Total 2 marks]
3.
Describe briefly the quark model of hadrons.
•
Illustrate your answer by referring to the composition of one
hadron.
•
Include in your answer the names of all the known quarks.
•
Give as much information as you can about one particular quark.
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[Total 5 marks]
4.
This question is about the properties of baryons.
Choose two examples of baryons
For each example discuss
•
their composition
•
their stability.
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[Total 6 marks]
5.
This question is about the properties of leptons.
Choose two examples of leptons
For each example discuss
•
their composition
•
the forces which affect them
•
where they may be found.
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[Total 6 marks]
Lesson 38 notes – Beta Decay
Objectives
(e) describe how there is a weak interaction between quarks and that this is
responsible for β decay;
(f) state that there are two types of β decay;
(g) describe the two types of β decay in terms of a simple quark model;
(h) state that (electron) neutrinos and (electron) antineutrinos are produced
during β+ and β- decays, respectively;
(i) state that a β- particle is an electron and a β+ particle is a positron;
(j) state that electrons and neutrinos are members of a group of particles
known as leptons.
Outcomes
Be able to state that there are two types of β decay.
Be able to state that a β- particle is an electron and a β+ particle is a positron.
Be able to describe the two types of β decay in terms of a simple quark
model.
Be able to state that (electron) neutrinos and (electron) antineutrinos are
produced during β+ and β- decays, respectively.
Be able to state that electrons and neutrinos are members of a group of
particles known as leptons.
Be able to describe how there is a weak interaction between quarks and that
this is responsible for β decay.
Be able to link ideas about Momentum into forces between particles.
Radioactivity
Alpha, Beta and Gamma are the 3 most common
forms of Nuclear Radiation. We will study this in
more detail later on but we are concentrating on
Beta decay in this lesson.
Beta Decay
Beta particles are electrons (or
positrons) emitted from a nucleus.
Beta Radiation comes with an
associated anti-neutrino that
shares the momentum and energy
of the decay. This is shown in the
before and after diagrams:
Beta decay is the decay of one of the neutrons to a proton via the weak
interaction:
Example:
Decay equation:
Quark Equation
udd → uud + e- + ῡ
This can be simplified to
d → u + e- + ῡ
Explanation:
The flow diagram above shows how a neutron changes into a proton and in
doing so emits an electron and an anti-neutrino. Beta decay occurs where
there is an unbalanced amount of protons and neutrons. (a free neutron is
unstable and will decay in about 15 minutes but in a nucleus with other
protons the binding energy (discussed in a later lesson) keeps the nuclei
stable).
1
A neutron (2 down quarks and an up quark).
2
One of the down quarks changes flavour to an up quark. The down
quark has a charge of -1/3 and the up quark has a charge of 2/3 so
a virtual W - boson (a particle associated with The Weak Force) is
needed, which carries away a (-1) charge (conserving charge).
3
4
5
The new up quark bounces back because of conservation of
momentum and we now have a proton (2 ups and a down).
The W - splits into an electron and an antineutrino (both leptons).
All three new particles: The proton, the electron and the antineutrino
move away from each other.
Positron Emission β+
Positron emmision happens when an up quark changes into a down quark.
Isotopes which increase in mass under the conversion of a proton to a
neutron, or which decrease by less than me, do not spontaneously decay by
positron emission.
Example:
The energy emitted depends on the isotope that is decaying; the figure of 0.96
MeV applies only to the decay of carbon-11. Isotopes that spontaneously
decay are used in PET (positive emission topography) scans – used in
medical diagnosis.
The Weak Force
Although there are 6 quarks, all matter in the universe seems to be made from
just the Up and Down Quarks, the least massive charged lepton (the electron)
and neutrinos. The weak force (or weak interaction) acts between quarks over
a very small distance and is responsible for the decay of massive quarks and
leptons into lighter quarks and leptons. When fundamental particles decay,
they disappear, being replaced by two or more different particles. The total of
mass and energy is conserved, although some of the original particle's mass
is converted into kinetic energy, and the resulting particles always have less
mass than the original particle that decayed.
When a quark changes flavour because of the weak interaction or a lepton
changes type (a muon changing to an electron, for instance), the carrier
particles of the weak interactions are the W +, W-, and the Z particles. The W's
are electrically charged and the Z is neutral.
Lesson 38 questions – Beta Decay
MOST
1.
(i)
Name the group of particles of which the electron and the positron
are members.
............................................................................................................
[1]
(ii)
Name another member of this group.
............................................................................................................
[1]
[Total 2 marks]
2.
Tritium-3 ( 31 H ) decays to helium-3 ( 32 He ) with the emission of a –
particle.
(i)
Name the force responsible for this decay process.
............................................................................................................
[1]
(ii)
Write a nuclear equation to represent this process.
[1]
(iii)
Write a quark equation, in its simplest form, to represent this
process.
[2]
[Total 4 marks]
3.
(a)
The table of Fig. 1 shows four particles and three classes of
particle.
hadron
baryon
lepton
neutron
proton
electron
neutrino
Fig. 1
Indicate using ticks, the class or classes to which each particle
belongs.
[2]
(b)
The neutron can decay, producing particles which include a proton
and an electron.
(i)
State the approximate half-life of this process.
..................................................................................................
[1]
(ii)
Name the force which is responsible for it.
..................................................................................................
[1]
(iii)
Write a quark equation for this reaction.
..................................................................................................
..................................................................................................
[2]
(iv)
Write number equations which show that charge and baryon
number are conserved in this quark reaction.
charge
.........................................................................................
..................................................................................................
baryon number
.....................................................................................
..................................................................................................
[2]
(c)
Fig. 2 illustrates the paths of the neutron, proton and electron only
in a decay process of the kind described in (b).
proton
neutron
electron
Fig. 2
Fig. 3 represents the momenta of the neutron, pn, the proton, pp and the
electron, pe on a vector diagram.
pe
pp
pn
Fig. 3
ALL
(i)
Draw and label a line on Fig. 3 which represents the resultant
pr of vectors pp and pe.
[1]
SOME
(ii)
According to the law of momentum, the total momentum of
an isolated system remains constant.
Explain in as much detail as you can, why the momentum pr
is not the same as pn.
..................................................................................................
..................................................................................................
..................................................................................................
..................................................................................................
..................................................................................................
..................................................................................................
[3]
[Total 12 marks]
Lesson 39 notes – Radioactive properties
Objectives
(a) describe the spontaneous and random nature of radioactive decay of
unstable nuclei;
(b) describe the nature, penetration and range of α-particles, β-particles and
γ-rays;
Outcomes
Be able to describe the spontaneous and random nature of radioactive decay
of unstable nuclei.
Be able to describe the nature, penetration and range of α-particles, βparticles and γ-rays.
Nuclear Radiation
Unstable nuclei break down and release different types of Nuclear Radiation.
The 3 most common are:
Alpha particles (α)
The emission of an alpha particle (a
helium nucleus), only occurs in very
heavy elements such as uranium,
thorium and radium. The reason alpha
decay occurs is because the nucleus
of the atom is unstable. With too many
protons that repel each other. In an
attempt to reduce the instability, an alpha particle is emitted. The alpha
particles are in constant collision with an energy barrier in the nucleus and
because of their energy and mass, there exists a nonzero probability of
transmission. That is, an alpha particle (helium nucleus) will tunnel out of the
nucleus of the heavy element.
Beta Particles (β)
Beta decay occurs when the
neutron to proton ratio is too
great in the nucleus and causes
instability. In basic beta decay, a
neutron is turned into a proton
and an electron. The electron is
then emitted.
There is also positron emission
when the neutron to proton ratio
is too small. A proton turns into a
neutron and a positron and the
positron is emitted. A positron is
basically a positively charged
electron.
Gamma Rays (γ)
After a decay reaction, the
nucleus is often in an
“excited” state. This means
that the decay has produced
a nucleus that still has
excess energy to get rid of.
Rather than emitting another
beta or alpha particle, this
energy is lost by emitting a
pulse of electromagnetic
radiation called a gamma
ray. The gamma ray is
identical in nature to light or
microwaves, but of very high
energy. Like all forms of
electromagnetic radiation,
the gamma ray has no mass
and no charge.
Gamma rays interact with material by colliding with the electrons in the shells
of atoms. They lose their energy slowly in material, being able to travel
significant distances before stopping. Depending on their initial energy,
gamma rays can travel from 1 to hundreds of meters in air and can easily go
right through people.
It is important to note that most alpha and beta emitters also emit gamma rays
as part of their decay process. There is no such thing as a “pure” gamma
emitter.
Nuclear Properties
Type of
Radiation
Alpha particle
Beta particle
Gamma ray
Symbol



Mass (atomic
mass units)
4
1/2000
0
Charge
+2
-1
0
Speed
Slow*
Fast**
very fast (speed of
light)
Ionising ability
high
medium
0
Penetrating
power
low
medium
high
Range (in air)
50mm
3m
Several kms
Stopped by:
paper
aluminium
lead
*An alpha particle emitted by a uranium nucleus has an initial speed of about
15 million meters/second (about 0.05 light speed.
**Beta particles travel with an initial speed of about 180 million m/s, or about
0.6 light-speed
Deflection in a magnetic/electric field.
When Alpha, Beta or Gamma travel through either field they will feel a force
as described in the diagrams:
Lesson 39 questions – Radioactive Properties
Name……………………………….
Class……………
ALL
1.
(a)
(
/17)…..%………
Complete the table below for the three types of ionising radiation.
radiation
nature
range in air
α
β
γ
penetration ability
0.2 mm of paper
electron
several km
[3]
(b)
Describe briefly, with the aid of a sketch, an absorption experiment
to distinguish between the three radiations listed above.
............................................................................................................
............................................................................................................
............................................................................................................
[3]
[Total 6 marks]
2.
State three ways in which decay by emission of an -particle differs from
decay by emission of a -particle.
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
[Total 3 marks]
3.
In this question, two marks are available for the quality of written
communication.
State and compare the nature and properties of the three types of
ionising radiations emitted by naturally occurring radioactive substances.
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
.....................................................................................................................
[6]
Quality of Written Communication [2]
[Total 8 marks]
Lesson 40 notes – Radioactive Decay and Half Life
Objectives
(c) define and use the quantities activity and decay constant;
(d) select and apply the equation for activity A = λN;
(e) select and apply the equations A = A0e-λt and N = N0e-λt where A is the
activity and N is the number of undecayed nuclei;
(f) define and apply the term half-life;
(g) select and use the equation λt1/2 = 0.693;
(h) compare and contrast decay of radioactive nuclei and decay of charge on
a capacitor in a C–R circuit (HSW 5b); See also lesson 25
(i) describe the use of radioactive isotopes in smoke alarms (HSW 6a);
(j) describe the technique of radioactive dating (ie carbon-dating).
Outcomes
Be able to describe the use of radioactive isotopes in smoke alarms (HSW
6a).
Be able to describe the technique of radioactive dating (ie carbon-dating).
Be able to define and apply the term half-life.
Be able to define and use the quantities activity and decay constant.
Be able to select and apply the equation for activity A = λN.
Be able to select and apply the equations A = A0e-λt and N = N0e-λt where A is
the activity and N is the number of undecayed nuclei.
Be able to select and use the equation λt1/2 = 0.693.
Be able to compare and contrast decay of radioactive nuclei and decay of
charge on a capacitor in a C–R circuit (HSW 5b). See also lesson 25
Be able to derive and apply the equations N = N0e-λt where N is the number of
undecayed nuclei.
Definitions
λ is the decay constant (s-1 ) is the fraction of substance that decays per
second, so it always is a number less than 1.
Activity, A is the number of radioactive emissions from a mass of substance /
unit time.
The unit is the Becquerel with 1 Bq = 1 emission /second
The Activity depends on two things: The mass of the substance and how
active the isotope is.
A= λN
A is the Activity (Bq)
N is the number of undecayed atoms of an isotope.
λ is the decay constant (s-1 ) Different isotopes have different decay
constants.
The received count rate, C is the number of emissions detected per unit time
with units of s-1 or Hz.
So, C  A
C = kA
(with k being related the sensitivity of the detector)
The rate of reduction of N, -dN/dt = λN
The solution to this is
N=N0e-λt
Where N0 is the original is the original number of undecayed atoms at t=0
since A= λN and C = kA
A=A0e-λt
C=C0e-λt
We cannot say which atom will decay but we can describe very accurately
how much of a substance will decay knowing the decay constant. The half-life
of a substance can then be found. This the time it takes for the number of
undecayed atoms in a substance to halve.
So we can write
From: N=N0e-λt1/2
N0 /2 =N0 e-λt1/2
½ = e-λt1/2
2 = eλt1/2
ln 2 = λt1/2
The half life for an isotope with decay constant λ is:
0.693 / λ = t1/2
Finding the decay constant graphically
N = N0e-λt
lnN=ln(N0e-λt)
lnN=lnN0 + ln(e-λt)
lnN=lnN0 -λt
lnN = -λt + lnN0
y = mx + C
In the form of
λ = m, the gradient
lnN0 = C, the intercept and N0 can be found by eC
Extension Derivation of A = A0e-λt
Where A is the radioactivity in nuclei per units of time (SI unit: Bq) after time t
has elapsed and A0 is the initial radioactivity.
Starting with
N = N0e-λt
A = dN/dt = -λN0e-λt
If t = 0
A0 = -λN0
Substitute:
A = -λN0e-λt
A = A0e-λt
Lesson 40 questions – Radioactive Decay and Half
Life
Name……………………
Class…………….
(
/45)……..%………
ALL
1.
The activity A of a sample of a radioactive nuclide is given by the
equation
A = N
Define each of the terms in the equation.
A ............................................................................................................
.....................................................................................................................
 ............................................................................................................
.....................................................................................................................
N ............................................................................................................
.....................................................................................................................
[Total 3 marks]
2.
The radioactive nickel nuclide
a half-life of 120 years.
(a)
63
28 Ni
decays by beta-particle emission with
A copper nucleus is produced as the result of this decay. State the
number of nucleons in the copper nucleus which are
protons
..................................................................................................
neutrons
..................................................................................................
[2]
(b)
Show that the decay constant of the nickel nuclide is 1.8 × 10–10s–1.
1 year = 3.2 × 107 s
[1]
(c)
A student designs an electronic clock, powered by the decay of
–12
nuclei of 63
F
28 Ni . One plate of a capacitor of capacitance 1.2 × 10
is to be coated with this isotope. As a result of this decay, the
capacitor becomes charged. The capacitor is connected across the
terminals of a small neon lamp. See Fig. 1. When the capacitor is
charged to 90 V, the neon gas inside the lamp becomes
conducting, causing it to emit a brief flash of light and discharging
the capacitor. The charging starts again. Fig. 2 is a graph showing
how the voltage V across the capacitor varies with time.
100
–12
1.2 × 10
V
F
neon
lamp
V/V
50
0
0
Fig. 1
(i)
1.0
2.0
Fig. 2
Show that the maximum charge stored on the capacitor is 1.1
× 10–10 C.
[2]
(ii)
When a nickel atom emits a beta-particle, a positive charge of
1.6 × 10–19 C is added to the capacitor plate. Show that the
number of nickel nuclei that must decay to produce 1.1 × 10–
10
C is about 7 × 108.
[2]
3.0
time / s
(iii)
The neon lamp is to flash once every 1.0 s. Using your
answer to (b), calculate the number of nickel atoms needed in
the coating on the plate.
number = .......................
[3]
(iv) State, giving a reason, whether or not you would expect the
clock to be accurate to within 1% one year after manufacture.
..................................................................................................
..................................................................................................
..................................................................................................
[1]
[Total 11 marks]
3.
Uranium-238
decays.
238
92 U
One nucleus of
decays to lead-206
238
92 U
206
82 Pb
by means of a series of
decays eventually to one nucleus of
206
82 Pb .
This means that, over time, the ratio of lead-206 atoms to uranium-238
atoms increases. This ratio may be used to determine the age of a
sample of rock.
In a particular sample of rock, the ratio
number of lead - 206 atoms
1
 .
number of uranium - 238 atoms 2
(a)
Show that the ratio
number of uranium - 238 atoms left
2
 .
number of uranium - 238 atoms initially 3
Assume that the sample initially contained only uranium-238 atoms
and subsequently it contained only uranium-238 atoms and lead206 atoms.
[2]
(b)
Calculate the age of the rock sample.
The half-life of
238
92 U
is 4.47 × 109 years.
age = ................................................ years
[3]
(c)
The rock sample initially contained 5.00 g of uranium-238.
Calculate the initial number N0 of atoms of uranium-238 in this
sample.
number = .........................................................
[2]
(d)
On the figure below, sketch graphs to show how the number of
atoms of uranium-238 and the number of atoms of lead-206 vary
with time over a period of several half-lives.
Label your graphs ‘U’ and ‘Pb’ respectively.
N0
number
of atoms
0
0
time
[3]
[Total 10 marks]
4.
The activity of the potassium source is proportional to the count rate
minus the background count rate, that is
activity = constant × (count rate – background count rate).
(i)
The radioactive decay law in terms of the count rate C corrected for
background can be written in the form
C = Coe–t
where  is the decay constant.
Show how the law can be written in the linear form
ln C = –t + lnCo
[2]
(ii)
Fig. 2 shows the graph of ln C against time t for the beta-decay of
potassium.
4.6
ln C
4.4
4.2
4.0
0
2
4
6
8
10
t/h
Fig. 2
Use data from the graph to estimate the half-life of the potassium
nuclide.
half-life = ………………….h
[3]
[Total 5 marks]
5.
A radioactive material is known to contain a mixture of two nuclides X and
Y of different half-lives. Readings of activity, taken as the material
decays, are given in the table, together with the activity of nuclide X over
the first 12 hours.
time / hour
activity of
material / Bq
activity of
nuclide X /Bq
activity of
nuclide Y /Bq
0
4600
4200
400
6
3713
3334
12
3002
2646
18
2436
24
1984
30
1619
36
1333
1323
296
(a)
State the meaning of the terms
(i)
radioactive
..................................................................................................
..................................................................................................
[1]
(ii)
nuclide
..................................................................................................
..................................................................................................
[1]
(iii)
half-life.
..................................................................................................
..................................................................................................
[1]
(b)
(i)
The half-life of nuclide X is 18 hours. Complete the activity of
nuclide X column.
[3]
(ii)
Using your answer to (i) complete the activity of nuclide Y
column.
[2]
(c)
Calculate, or use a graph to determine, the half-life of nuclide Y.
0
20
40
60
80
time/hour
half-life of Y = ......................... hours
[3]
(d)
Indicate briefly how it would be possible experimentally to obtain
the initial activity (4200 Bq in this case) of nuclide X by itself.
............................................................................................................
............................................................................................................
............................................................................................................
[2]
(e)
Explain why it is not possible to give a half-life for a mixture of two
nuclides.
............................................................................................................
............................................................................................................
............................................................................................................
............................................................................................................
............................................................................................................
............................................................................................................
............................................................................................................
[3]
[Total 16 marks]
Lesson 41 notes – Binding energy and E=mc2
Objectives
(a) select and use Einstein’s mass–energy equation ΔE = Δmc2 ;
(b) define binding energy and binding energy per nucleon;
(c) use and interpret the binding energy per nucleon against nucleon number graph;
(d) determine the binding energy of nuclei using ΔE = Δmc2 and masses of nuclei;
Outcomes
Be able to select and use Einstein’s mass–energy equation ΔE = Δmc2 .
Be able to define binding energy and binding energy per nucleon.
Be able to use and interpret the binding energy per nucleon against nucleon number
graph.
Be able to determine the binding energy of nuclei using ΔE = Δmc2 and masses of
nuclei.
Be able to derive E=mc2 from Einstein’s theory of Special Relativity!
Einstein
Einstein’s Special theory of relativity says that matter and energy are equivalent
Energy = mass x speed of light squared or E = mc2
E is the amount of energy produced when a mass m is completely converted to energy
and c is the speed of light (3x108 ms-1).
Binding energy and mass defect
If you take an atom and split it into its bits (protons and neutrons), the mass
before does not equal the mass of all the individual bits!
For a nucleus this difference in mass is called the mass defect of the nucleus.
Below is a table of some mass defects:
The difference in mass is the difference in energy it takes to split the atom up given
by E = mc2. This is called the binding energy of a nucleus.
Mass defect = (unbound system calculated mass) - (measured mass of nucleus)
The energy given off during either nuclear fusion or nuclear fission is the
difference between the binding energies of the fuel and the fusion or fission
products.
Binding Energy per Nucleon
The Graph of Binding Energy per Nucleon against Nucleons in the Nucleus
shows that, generally, from Hydrogen up until Sodium, the binding energy per
nucleon increases as the number of nucleons in the nucleus are added. This
is due to the Strong Force exerting itself on each nucleon and binding them all
together tightly.
From magnesium to xenon, the nuclei have become large enough that
nuclear forces no longer completely extend efficiently across their widths.
Attractive nuclear forces in this region, as atomic mass increases, are nearly
balanced by repellent electromagnetic forces between protons, as atomic
number increases.
In elements heavier than xenon, there is a decrease in binding energy per
nucleon as atomic number increases. In this region of nuclear size,
electromagnetic repulsive forces are beginning to become bigger than the
attractive strong nuclear force that exists between all nucleons.
Nickel-62 is the most tightly-bound nucleus (per nucleon), followed by iron-58
and iron-56. This is the basic reason why iron and nickel are very common
metals in planetary cores, since they are produced as end products in
supernovae and in the final stages of silicon burning in stars.
Extension – derivation of E = mc2
The Einstein equation (E = mc2) can be deduced from special relativity as
follows:
m = mo/[1 - v2/c2]1/2 therefore m2c2 – m2v2 – moc2 = 0 where mo is the rest
mass of the object.
Differentiating with respect to time gives: c2 2m[dm/dt] – 2mv[d(mv)/dt] = 0
Rearranging this equation gives: c2 2m[dm/dt] = 2mv[d(mv)/dt]
and therefore c2[dm/dt] = v[d(mv)/dt]
However dE/dt = Fv and so dE/dt = Fv = v[d(mv)/dt] = c2dm/dt
And so E = mc2
Lesson 42 notes - Fission and Fusion
Objectives
(e) describe the process of induced nuclear fission;
(f) describe and explain the process of nuclear chain reaction;
(g) describe the basic construction of a fission reactor and explain the role of
the fuel rods, control rods and the moderator (HSW 6a and 7c);
(h) describe the use of nuclear fission as an energy source (HSW 4 and 7c);
(i) describe the peaceful and destructive uses of nuclear fission (HSW 4 and
7c);
(j) describe the environmental effects of nuclear waste (HSW 4, 6a and b, 7c);
(k) describe the process of nuclear fusion;
(l) describe the conditions in the core of stars
Outcomes
Be able to describe the process of induced nuclear fission;
Be able to describe and explain the process of nuclear chain reaction;
Be able to describe the basic construction of a fission reactor and explain the
role of the fuel rods, control rods and the moderator (HSW 6a and 7c);
Be able to describe the use of nuclear fission as an energy source (HSW 4
and 7c);
Be able to describe the peaceful and destructive uses of nuclear fission (HSW
4 and 7c);
Be able to describe the environmental effects of nuclear waste (HSW 4, 6a
and b, 7c);
Be able to describe the process of nuclear fusion;
Be able to describe the conditions in the core of stars
Fission
An unstable nucleus may become stable and lose the extra energy in two ways:
It can emit radiation (alpha, beta or gamma) or undergo fission. In nuclei there
are two competing forces: The Strong Nuclear Force, which is an attractive force
that acts between all nucleons; and the electrostatic force that repels the
positive protons from each other.
Induced nuclear fission
The above diagram shows how in induced nuclear fission a slow moving
neutron is fired at Uranium 235 so that it becomes uranium 236 which is
unstable and so splits into to fission particles, 2-3 neutrons and Energy (in the
form of Gamma and Heat).
Chain Reaction
The diagram shows how, because of the emission of 2-3 neutrons in each
fission reaction, a chain reaction occurs.
Nuclear Fission Reactor
The fission reaction occurs in the reactor that is shielded with concrete. The
fuel rods are of a material such as 235U. 235U is stable but can be made
unstable by adding a neutron. A fast neutron from a neutron source (such as
californium) must be slowed down (moderated) so that it can be absorbed.
Graphite is used as a moderator by placing it in between the fuel rods so that
as a neutron collides with the nuclei of the graphite it bounces about and
loses momentum so slowing it down. When the neutron is absorbed 236U is
formed which is unstable and so it splits (fissions) into 2 daughter nuclei, 2 or
3 neutrons and lots of energy in the form of heat and gamma rays:
235U
+ 1n → 236U → 92Kr + 142Ba + 21n+ Energy
The heat boils up water which turns into steam, which turns turbines and
generators and produces electricity.
If the electricity production needs to be slowed done, Boron rods are placed
into the reactor that can absorb some of the stray neutrons and so reduce the
amount of heat and therefore electricity.
Nuclear Fusion
Introduction
Nuclear fusion is the process of binding nuclei together to form heavier nuclei
with the release of energy. It is the process that powers the stars and our own
Sun.
Fusing Nuclei
Protons won’t stick together easily because they are both positive and so
repel each other. The strong force will win over very short distances but you
need to give the protons a lot of energy to over come the repulsion before the
can fuse. This means very high temperatures.
Extension – Estimating the temperature needed:
The magnitude of the force between protons is given by:
F= (k q1 q2)/r2
where k=1/(4πε0) is the Coulomb constant = 8.988×109 m F-1.
The work done, U in moving the two protons together until they are attracted
by the strong force is given by:
U= (k q1 q2)/r0.
The Coulomb barrier increases with increasing atomic number.
U=(k Z1 Z2 q2)/r0.
Where Z1 and Z2 are the proton numbers of the nuclei being fused.
Using figures for 2 Deuterium nuclei, for which Z1,2=1, we obtain:
U= (8.988 x 109 x 1 x 1 x (1.6 x 10-19) 2)/(1 x 10-15) = 2.298 x 10-13 J
The kinetic energy of the nuclei is related to the temperature by:
(1/2) mv2 = (3/2) kBT
By equating the average thermal energy to the Coulomb barrier height and
solving for T, gives a value for the temperature of around 1.1 x 1010 K.
Nuclear Fusion in Stars
In 1848, J.R. Mayer examined the then-popular theory of the Sun being
composed of burning coal. He stated that if the Sun began burning 5000
years ago, corresponding to the Biblical age of the Earth, then by his
calculations, it already would have burned out.
Lord Kelvin proposed several explanations on how the Sun might generate its
energy including: mass contraction, which could allow the Sun to shine for up
to 45 million years.
Charles Darwin was looking at the erosion of rocks and concluded that the
Earth had to be at least 300 million years old. The Sun had to be at least as
old as the Earth so clearly the solution had not been found.
Missing Mass
It was discovered that the when nuclei of hydrogen combine to form Helium,
the resulting mass was less than the sum of the mass entering the sum of the
initial masses. The missing mass was converted into energy with an
exchange rate of E=Δmc2 where Δm is the difference in the mass of the
nuclear reaction and c is the speed of light (3 x 108 m s-1). The conversion of a
relatively small amount of mass into energy would allow the Sun to shine for
billions of years.
The fusion of Hydrogen into Helium in stars occurs in three stages:
First, two ordinary Hydrogen (Hydrogen-1) nuclei, which are actually just
single protons, fuse to form an isotope of Hydrogen called Deuterium
(Hydrogen-2), which contains one proton and one neutron. A positron (a
positively charged electron) and a neutrino (a neutral particle which travels
nearly at the speed of light and has, perhaps, almost no mass) are also
produced. The positron is very quickly annihilated in the collision with an
electron and the neutrino travels right out of the Sun.
1 H
1
+11H = 21H+ 00e+ +00ν
The newly-formed Deuterium fuses with another regular Hydrogen to form an
isotope of Helium, Helium-3 containing two protons and one neutron.
2 H+ 1 H
1
1
= 31H
Next, two of the Helium-3 nuclei fuse to form a Helium-4 nucleus and two
hydrogen-1 nuclei. Energy as gamma rays are produced in each step.
3 H+3 H = 4 He + 21 H
1
1
2
0
The resulting reaction cycle generates around 25 MeV of energy. The high
density of the Sun allow the temperature for fusion to occur to be around 1.5 x
107 K
Nuclear Fusion on Earth
Man-made nuclear fusion uses a different reaction to that which occurs in the
stars. In stellar Hydrogen burning, the reaction of two Helium-1 nuclei requires
a proton to change into a neutron. Fusion on Earth starts by fusing Deuterium
and Tritium. (Tritium is an isotope of Hydrogren which contains 1 proton and 2
neutrons.) The reaction is as follows:
2 H
1
+ 31H = 42He + 10n + 17.59 MeV.
An equally probable reaction can also occur between two Deuterium nuclei in
one of two ways:
2 H +2 H = 3 H + 1 n + 3.27 MeV
1
1
2
0
or alternatively,
2 H
1
+21H = 31H + 4.03 MeV
Nuclear Fusion Reactors
The Tokamak
The tokamak uses magnetic fields to confine high temperature plasma to the
interior of a torus shaped vacuum chamber. When the plasma has been
heated to around 100 million K fusion occurs. Each fusion reaction results in
the production of an alpha particle (42He nucleus) and a neutron. The
neutrons carry most of the energy and can escape the confining fields. They
are captured in the walls of the tokamak where they generate heat. A coolant
circulating through the walls is passed through a heat exchanger to produce
the steam to drive turbines, as in a conventional power station. The walls also
double as a "breeding blanket" in which neutrons react with Lithium to
produce further Tritium.
Figure 2. A Tokamak design of fusion reactor
From: www.splung.com/content/sid/5/page/fusion
Lesson 42 practice questions – Fission and Fusion
1
In nuclear fission, energy is released.
a)
Explain what is meant by nuclear fission.
…………………………………………………………………………………………
…………………………………………………………………………………………
……………………………………………………………………………………… (1)
b)
In a possible fission reaction Uranium 235 (atomic number 92)
captures a neutron to become a compound nucleus before splitting into Ba 141
(atomic number 56) and Kr 92 (atomic number 36) releasing three neutrons.
Write down the nuclear reaction equation for this event.
……………………………………………………………………………………… (2)
c)
The total mass of the compound nucleus Uranium 236 (atomic number
92) before fission is 236.053u. The total mass of the fission products is 235.867u. Use
these data to calculate the energy released in the fission process. (1u=1.66054x1027
kg)
energy = ……………………….. J (3)
2
a)
A possible fission reaction is
i)
The two asterisks represent two numbers missing from the right hand
side of the nuclear reaction.
Write down the missing nucleon (atomic mass) number
…………………………..
and the missing proton (atomic) number
…………………………………………..
ii)
The total mass of the compound nucleus
before fission is
236.053u. The total mass of the fission products is 235.840u. Show that the energy
released in the fission process is about 3 x 10-11J.
(3)
3
One of the reactions that fuel the stars is the fusion of two protons to give deuterium.
In turn the deuterium goes through a series of reactions, the end product being helium. This is
also a process that releases energy. In this question you are asked to consider the energy
that would be released if all the deuterium in the water contained in an electric kettle were to
be converted by fusion into helium.
The kettle contains 1 litre of water. The data you need are listed below.
1 atomic mass unit (u) = 931 MeV
–19
1 eV = 1.6  10
NA = 6.02 × 10
a
23
J
–1
mol
Particle
Mass / u
1
1H
1.007 825
2
1H
2.014 102
3
2 He
3.016 030
1
0n
1.008 665
3
2
Two deuterium nuclei 1 H can fuse to give one nucleus of helium 2 He with the
ejection of one other particle. Write down the balanced equation that represents this
reaction.
b
Calculate the mass change that occurs in this reaction.
c
Convert this energy into joules.
This gives you the energy released when two deuterium nuclei fuse. The next steps take you
through the calculation of the total energy released if all the deuterium in the kettle water were
to fuse to make helium-3. The ratio of deuterium atoms to hydrogen in water is roughly 1 to
7000.
d
What is the mass of 1 mole of water (H = 1 u; O = 16 u roughly)?
e
How many moles of water are contained in the litre?
f
How many molecules of water (H2O) are in the kettle?
g
How many molecules of deuterium oxide (D 2O) are in the kettle?
h
Each heavy water molecule has two atoms of deuterium; what total energy is
released if all the deuterium in the kettle is converted to helium-3?
Now to put this number in a new perspective. It requires 4200 J to increase the temperature
of 1kg of water by 1K.
i
How many litres of water could be heated through 100 K by the fusion energy you
calculated in question 8?