Part 1- Properties of alpha, beta, and
gamma radiation
The discovery of the nucleus
Write down 4 facts about nuclei:







Contains protons and neutrons
These are called nucleons
Protons and neutrons are made from quarks (uud and udd)
Protons and neutrons are baryons
The nucleus has a diameter of around 10-15 m
It is positively charged
Its composition determines:
 The element
 Its stability
How do we know this?!
Rutherford
The previous idea was J.J. Thomsons
“plum pudding” model, where a
sphere of diffuse (spread out)
positive charge had electrons
randomly placed inside it.
Alpha particles were considered to
be nuclear sized bullets that would
smash the atoms in the gold foil like
watermelons, because they had too
much energy to be deflected by the
diffuse charges in the atom.
http://phet.colorado.edu/en/si
mulation/rutherfordscattering
Instead, they found that many alpha
particles were deflected slightly,
while a few came back in the
direction they came from.
Rutherford
Conclusions:
- There is a positively charged
nucleus, which is a very
small, concentrated area of
positive charge (necessary
to have enough repulsion to
bounce alpha particles
backwards!)
- The nucleus is very tiny
compared with the rest of
the atom; most of the atom
is just empty space.
- The radius of a nucleus was
in the order of ~ 10-15 m.
Radioactivity
Radioactivity and Ionising Radiation
The nuclei of some isotopes are
unstable and when they decay
they give off radiation that
causes ionisation.
This phenomena is called
radioactivity and the radiation
produced is called ionising
radiation
Radioactivity is a random
process. When a particular
nucleus decays cannot be
predicted.
Henri Becquerel discovered
radioactivity in 1896
The properties of nuclear radiation
What do the observations in the diagram
say about the properties of radiation?
Deflection by electric fields
-
-
-
Alpha and beta particles are
deflected in opposite
directions due to their
opposite charges.
Due to their much smaller
mass, beta particles are
deflected far more than alpha.
+ + +
Electric field produced by
positively and negatively
charged plates
Gamma rays are not deflected
because they are not
charged.
Deflection by magnetic fields
S
Magnetic field “into”
diagram
Alpha and beta particles are
deflected in opposite
directions due to their
opposite charges.
Due to their much smaller
mass, beta particles are
deflected far more than alpha.
Gamma rays are not deflected
because they are not
charged.
The penetrating power of
alpha, beta and gamma radiation
Paper or 2-5 cm
of air stops alpha
particles
1m of air or 1cm of
aluminium stops
beta particles
Several cm of lead or 1m
of concrete is needed to
stop gamma rays
What do the observations in the diagram
say about the properties of radiation?
Alpha radiation (α)
• Usually occurs with very large nuclei e.g. uranium
238
• An alpha particle consists of 2 protons plus 2
neutrons
• After decay:
– Proton number (Z) decreases by 2
– Nucleon number (A) decreases by 4
• General equation for decay:
• Example:
A
X
Z
238
92 U
→
→
A-4
Y
Z-2
234
Th
90
+
+
4
2
4
α
2
α
Beta radiation (β -)
• Occurs with nuclei that have too many neutrons e.g. carbon
14
• A Beta particle consists of a fast moving electron
• In the nucleus a neutron decays into a proton and an
electron.
• The electron is emitted as the beta minus particle
• An antineutrino is also emitted
• After decay:
– Proton number (Z) increases by 1
– Nucleon number (A) does not change
• General equation for decay:
A
• Example:
Z
X →
14 C → 14 N
7
6
A
Y
Z+1
0
+ - 1 e - + 𝜐𝑒
+ 0 e - + 𝜐𝑒
-1
Beta radiation (β +)
• Occurs with nuclei that have too few neutrons e.g.
Sodium-20
• The beta particle here consists of a fast moving positron
• In the nucleus a proton decays into a neutron and a
positron
• The positron is emitted as the beta plus particle
• An neutrino is also emitted
• After decay:
– Proton number (Z) decreases by 1
– Nucleon number (A) does not change
• General equation for decay:
A
• Example:
Z
X →
A
Y
Z-1
20 Na → 20 Ne + 0 e+ + 𝜐
𝑒
10
11
+1
0
+ + 1 e+ + 𝜐𝑒
Gamma radiation (γ)
• This is electromagnetic radiation emitted from
an unstable nucleus.
• Gamma radiation often occurs straight after
alpha or beta decay. The child nuclide formed
often has excess energy which is released by
gamma emission.
• No change occurs to either the proton or
nucleon numbers as a result of gamma decay.
Answers:
Complete:
1.
2.
3.
4.
19
8
239
94
231
92
102
45
19
O →
9
235
Pu →
U→
92
231
Rh →
91
98
43
F +
0
-1
4
U +
Pa +
Tc +
2
0
+1
4
2
e-
+
0
0
𝜐𝑒
α
e+
α
+
0
0
𝜐𝑒
The Ionisation chamber/Geiger tube
Ionisation occurs when an atom loses or
gains one or more electrons.
Ionising radiation literally “knocks”
electrons away from the air particles that
it passes.
Air ions created can then move to the
oppositely charged electrode in the
chamber, creating a current. This is how
Rutherford compared the ionisation of
Alpha, Beta and Gamma sources.
Alpha radiation has the highest mass and
charge, and therefore “knocks” electrons
and ionises the most.
A typical Geiger tube can detect separate
particles as long as they arrive more than 200
μs apart- therefore what is the maximum
count rate?
anode
low pressure neon gas
+450 V
0V
end window
end
window
anode
radioactive
particle
5000 counts per second.
Corrected Count rates
It’s worth noting that
when measuring count
rates (the number of
radioactive particles
hitting our geiger counter
every second), we need
to minus “background
radiation”
- This radiation is
constantly present
- Measure it first
without the source
present
- Then minus it from all
count rate values
Cloud chambers – the diffusion
chamber
felt ring
air saturated
with meths
vapour
solid carbon
dioxide
foam
rubber
alpha
source
When a radioactive
particle passes
through air which is
supersaturated with
the vapour of a
liquid the ions, it
produces act as
centres on which the
liquid can condense,
and so a line of liquid
droplets is formed
along the track of
the particle.
Cloud chamber tracks
Match the following labels to
the tracks
Cosmic ray track
Alpha collision with
gas molecule
Alpha source
What is the length of the track
proportional to?
The length of the track is proportional to the
energy of the particle.
What shape are  tracks?
Alpha particle
track
More “wispy”- easily deflected and
less ionising
Properties of Radiation Summary
Penetration
Ionisation
Effect of E or
B field
Few cm air
Thin paper
Intense,
about 104
ions per mm.
Slight
deflection as
it is a positive
charge
Beta-
High speed
electron
Q = -1 e
(or +1e for
Beta+)
Few mm of
aluminium
Less intense
than a, about
102 ions per
mm.
Strong
deflection in
opposite
direction to
α.
Gamma
Electromagnetic
wave
Several cm
lead, couple
of m of
concrete
Weak
interaction
about 1 ion
per mm.
No effect.
Radiation
Description
Alpha
Helium
nucleus
2p + 2n
Q=+2e
Inverse square law
What inverse square laws have you already met?
What is intensity?
Intensity is the radiation energy
passing normally through unit area per
second
What unit would it have?
Wm-2 or Js-1m-2
What is the equation for
photon energy?
E = hf
If n = number of photons per
second, how much energy
do we have per second?
Total Energy per second = nhf
What is the equation for the
surface area of a sphere?
A = 4r2
Inverse square law
Intensity is total
energy per second
per unit area:
𝐼=
𝑛ℎ𝑓
4𝜋𝑟 2
𝑘
𝐼= 2
𝑟
Or more commonly, we use a
proportionality constant k:
I in Watts per metre squared (Wm-2)
𝑛ℎ𝑓
4𝜋
K is
in Watts (W)
r metres (m)
If we take 𝐼1 =
𝑘
𝑟12
and 𝐼2 =
𝑘
𝑟22
𝐼2 𝑟12
= 2
𝐼1 𝑟2
and divide them:
Intensity
What is the value of 𝐼2 at
a) r2 = 2r1
𝐼2 =
𝑟12
𝑟22
𝐼1 =
𝑟12
𝐼
2𝑟1 2 1
1
𝐼2 =
𝐼1
4
b) r2 = 3r1
r0
1
𝐼2 =
𝐼1
9
As d increases, the intensity
decreases as 1/r2
2r0
3r0
Question 1
At a distance of 2m from a gamma source, the
intensity is 5 𝑊𝑚−2 . What distance would you need to
be for the Intensity to be 12 𝑊𝑚−2 ?
𝐼2 𝑟12
= 2
𝐼1 𝑟2
→
𝑟22
𝑟22
𝐼1
= × 𝑟12
𝐼2
5
=
× 22
12
𝑟22 = 1.6667
𝑟2 = 1.29𝑚
Question 2
At a distance of 20cm from a gamma source, the
intensity is 1.6 𝜇𝑊𝑚−2 . At what distance will the
intensity drop to 0.1 𝜇𝑊𝑚−2 ?
𝐼2 𝑟12
= 2
𝐼1 𝑟2
→
𝑟22
𝐼1
= × 𝑟12
𝐼2
−6
1.6
×
10
2
𝑟22 =
×
0.2
0.1 × 10−6
𝑟22 = 0.64
𝑟2 = 0.8𝑚
Dangers of radioactivity
Draw a diagram of a film
badge, explain its use, and
how it works:
Different area of the film have
different absorbers (different
materials) of varying
thicknesses in front of them
The amount of developed film
can be used to estimate
exposure to each type of
radiation
Name two areas of work
where such a badge might
be used:
Biological effects of radiation
Using the text on p 159-160 comment on the
biological effects of each type of radiation:
Ionising radiation can destroy
cell membranes, or damage
DNA
- Alpha radiation is the most damaging INSIDE the body, as it is the most ionising.
- However, Alpha is the least ionising OUTSIDE the body as it cannot penetrate dead
skin cells
- Alpha radiation outside the body may get on hands, and then eaten, so safety
precautions need to be taken
Describe safe storage and
handling of radioactive sources in
the laboratory:
 replace sources in sealed, lead-lined
containers as soon as possible
 always handle sources with tongs
 point the sources away from your body
(and not at any anybody else)
 fix the source in a holder which is not
adjacent to where your body will be when
you take measurements
 wash your hands when finished
Background Radiation
0.4
0.75
0.3
0.3
0.02
0.25
soil and building
materials
cosmic ray
showers
medical X-rays
Food and drink
(internal)
Nuclear industry
radon in air
(indoors)
The diagram shows how the annual
radiation dose equivalent of 2 mSv is
made up for people living in the UK.
1 Sievert (Sv) is the equivalent of your
body absorbing 1 Joule of radioactive
energy per kilogram of mass
In the year following the Chernobyl accident, the
average dose across the whole country increased
by around 0.1 mSv.
Dose comparison
80 mSv
250 mSv
500 mSv
670 mSv
1 Sv
5 Sv
21 Sv
54 Sv
6 months stay on the International Space
Station
6-month trip to Mars - radiation due to
cosmic rays, which are very difficult to
shield against
The U.S. occupational dose limit, shallowdose equivalent to skin, per annum
Highest dose received by a worker
responding to the Fukushima emergency
Maximum allowed radiation exposure for
NASA astronauts over their career
Fatal doses during Chernobyl accident (5
Sv per hour!)
Fatal acute dose to Louis Slotin in 1946
criticality accident
Fatal acute dose to Boris Korchilov in 1961
after a reactor cooling system failed on
the Soviet submarine K-19 which required
work in the reactor with no shielding
Half-life
Half-life
• If a warehouse has exactly two million copies
of the game “half-life” in it, and it sells half
each day, how many days will it take them to
sell the final copy (it can only sell “whole”
copies” of the game)?
Randomness
- Perhaps one of the weirdest things about
radioactivity is its inherent “randomness”
- We currently have NO WAY of ever predicting when a
particular, individual nuclei will actually decay
- What’s more, there are theories (Bell’s Theorem)
which seem to prove that we might never be able to
know…
- This was particularly unsettling to many Physicists,
including Einstein, who adamantly stood by the
famous phrase:
Half-life T1/2
• It is impossible to predict when one
particular atom will decay, but we can get an
extraordinarily accurate guess at how many
will decay when we use a large sample
• The half-life T1/2 is the time taken for half the
radioactive atoms in a sample to decay
• We can plot this information on a graph
Half-lives of some radioactive isotopes
Uranium 238 = 4500 million years
Uranium 235 = 704 million years
Plutonium 239 = 24 100 years
Carbon 14 = 5600 years
Strontium 90 = 29 years
Hydrogen 3 (Tritium) = 12 years
Cobalt 60 = 5.2 years
Technetium 99m = 6 hours
Radon 224 = 60 seconds
Helium 5 = 1 x 10-20 seconds
Example 1 - The decay of
a sample of strontium 90
Strontium 90 has a half-life of 29
years.
Year
Mass of
strontium 90 (g)
In 2012 a sample contains 18.2g
of strontium 90
2012
18.2
2041
9.10
The mass of strontium 90 in the
sample halves every 29 years.
2070
4.55
2099
2.27
2128
1.14
2157
0.57
When will the mass have fallen to 0.15 g?
2215
Remaining mass (m)
m = (0.5)n m0
Remaining mass, m is measured in kilograms (kg)
Original mass, m0 is measured in kilograms (kg)
Number of half-lives, n is unitless
Question 1
At 10am in the morning a radioactive sample contains
160g of a radioactive isotope. If the isotope has a halflife of 20 minutes calculate the mass of the isotope
remaining at 11:20am.
10am to 11:20am = 80 minutes
n = 80 / 20 minutes = 4 half-lives
Remaining mass of isotope m = (0.5)n X m0
m = (0.5)4 X 160g
mass at 11:20 am = 10g
Question 2
A sample contains 8 billion nuclei of hydrogen-3
atoms. Hydrogen-3 has a half-life of 12 years. How
many nuclei should remain after a period 60 years?
n of half-lives = 60 / 12 = 5
n=5
nuclei left = (0.5)5 x 8 billion
nuclei left = 250 million
(The equation works with number of nuclei, rather
than mass, as they are directly proportional!)
Question 3
Calculate the half-life of the radioactive isotope in a
source if its mass decreases from 48g to 3g over a
period of 60 days.
48g x ½ = 24g
24g x ½ = 12g
12g x ½ = 6g
6g x ½ = 3g
therefore FOUR half-lives occur in 60 days (n = 4)
half-life T1/2 = 60 / 4 = 15 days
Question 3
Calculate the half-life of the radioactive isotope in a
source if its mass decreases from 48g to 3g over a
period of 60 days.
Alternate method for finding n:
𝑚 = (0.5)𝑛 𝑋 𝑚0
𝑚
= 0.5𝑛
𝑚0
log 0.5
𝑚
=𝑛
𝑚0
n = log 0.5
3
=4
48
Half-life Graphs
Estimate the half-life
of the substance
whose decay graph is
shown opposite.
The half-life T1/2 is
approximately 20
seconds
Dice experiment
• You have 100 dice (between two), each one
representing a radioactive atom
• Roll the dice, and if any lands with the number 1
facing upwards, it has decayed (remove it from
the sample)
• Count how many are left and
record this in a table
• Roll them again and repeat!
• Also record the roll on which the special red dice
lands on “one” (and remove it)
Half-life T1/2
• 10% of the atoms in a radioactive substance
decay every hour.
– Make a table that shows the number of
radioactive atoms left after every hour (for a total
of ten hours) if we start with 1000 radioactive
atoms
– Plot this on a graph and calculate the half life from
at least three points on the graph
Activity
The activity of a radioactive source is
equal to the number of decays per
second.
∆𝑁
𝐴=
∆𝑡
Activity, A is measured in Bequerels (Bq)
Number of decays, ∆𝑁 is unitless
Change in time, ∆𝑡 is measured in
Seconds (s)
(1 Becquerel = 1 decay per second)
Henri Becquerel
discovered radioactivity
in 1896
Question 4
A radioactive source undergoes 72 000 decays over a
ten minute period.
What is its average activity in becquerels?
Activity in becquerels is decays per second.
∆𝑁 = 72 000
∆𝑡 = 10 X 60 = 600s
∆𝑁
𝐴 = = 72 000 / 600
∆𝑡
= 120 decays per second
Activity = 120 Bq
Question 5
A radioactive source has an activity of 25 Bq.
How many decays would be expected over a 3 hour
period?
𝐴 = 25 Bq
∆𝑡 = 3 X (60 X 60)= 10800s
∆𝑁
𝐴=
∆𝑡
∆𝑁 = 𝐴∆𝑡 = 25 X 10800
Number of decays ∆𝑁 = 270 000
Activity and Power
5MeV
5MeV
5MeV
5MeV
5MeV
For a radioactive source of Activity A, that emits particles
(or photons) of the same Energy E, we can define the
Power of the radioactive source:
∆𝐸𝑛𝑒𝑟𝑔𝑦 ∆𝑁𝐸
𝑃=
=
= 𝐴𝐸
∆𝑡𝑖𝑚𝑒
∆𝑡
𝑃 = 𝐴𝐸
(For the example above, each particle has Energy E = 5MeV!)
Predicting randomness
- The decay of each radioactive nuclei is a random
process, and the probability of it happening depends
of the half-life of the substance
- The Number of nuclei that decay in a sample, ∆𝑁, is
proportional to:
- the number of nuclei in the sample 𝑁
- the time interval ∆𝑡
∆𝑁 = −𝜆𝑁Δ𝑡
- 𝜆 is the decay constant, and the negative sign (-)
represents a decrease in the number of nuclei
- What is the Unit?
s-1
Decay equations
- So:
∆𝑁 = −𝜆𝑁Δ𝑡
- Solve for N:
𝑑𝑁
= −𝜆 𝑑𝑡
𝑁
ln 𝑁 = −𝜆𝑡 + 𝐶
𝑁 = 𝑒 −𝜆𝑡+𝐶
𝑁 = 𝑒 −𝜆𝑡 𝑒 𝐶
𝑁 = 𝑁0 𝑒 −𝜆𝑡
Decay equations
𝑁 = 𝑁0 𝑒 −𝜆𝑡
This tells us how many particles will be left (𝑁), from a
sample of 𝑁0, after time 𝑡.
Also starting from the equation at the top of the
previous page:
∆𝑁 = −𝜆𝑁Δ𝑡
∆𝑁
𝐴=
= −𝜆𝑁
∆𝑡
𝐴 = −𝜆𝑁
Decay equations
𝑁 = 𝑁0 𝑒 −𝜆𝑡
𝐴 = −𝜆𝑁
𝐴 = −𝜆 𝑁0 𝑒 −𝜆𝑡
𝐴 = 𝐴0 𝑒 −𝜆𝑡
(Note: we usually quote
Activity as a positive
quantity, though as you
can see here, it’s
negative because there
is a decrease in
number of nuclei!)
Finally, as mass is proportional to the number of nuclei
in a sample:
𝑚 = 𝑚0 𝑒 −𝜆𝑡
𝐶 = 𝐶0 𝑒 −𝜆𝑡
C=Count rate!
Question 6
Calculate the activity of a radioactive source containing 4 ×
1015 nuclei and with a decay constant of 3.0 × 10−8 s-1.
𝐴 = 𝜆𝑁
𝐴 = 3.0 × 10−8 4 × 1015
𝐴 = 1.2 × 108 Bq
Question 7
A radioactive source with a decay constant of 4 × 10−4 s-1
has 6 × 1020 nuclei at time t=0. Find how many nuclei there
are at:
(i) t=200s
(ii) t=5 hours
(i) 𝑁 = 𝑁0 𝑒 −𝜆𝑡
20
−(4×10−4 )(200)
𝑁 = 6 × 10 × 𝑒
𝑁 = 5.54 × 1020
(ii) 𝑡 = 5 × 60 × 60 = 18000𝑠
𝑁 = 𝑁0 𝑒 −𝜆𝑡
−4 )(18000)
20
−(4×10
𝑁 = 6 × 10 × 𝑒
𝑁 = 4.48 × 1017
Question 8
A radioactive source starts with 14000 Bq activity at t=0, but
has 4000 Bq at time t=100s. Find the decay constant:
𝐴 = 𝐴0 𝑒 −𝜆𝑡
𝐴
= 𝑒 −𝜆𝑡
𝐴0
𝐴
ln
= −𝜆𝑡
𝐴0
𝐴
ln
𝐴0
𝜆=
−𝑡
𝜆 = 0.0125 s-1
4000
ln
14000
=
−100
Decay constant 𝜆
The decay constant 𝜆 is the probability of an individual
nucleus decaying per second.
The LONGER the Half-life, the SMALLER the decay
constant (probability of decay per second is smaller!).
We can define a relationship between the two:
𝑁 = 𝑁0 𝑒 −𝜆𝑡
𝑁
= 𝑒 −𝜆𝑡
𝑁0
𝑁
ln
= −𝜆𝑡
𝑁0
Decay constant 𝜆
𝑁
ln
= −𝜆𝑡
𝑁0
At one half-life 𝑡 = 𝑇1/2 :
Also, 𝑁 = half of 𝑁0 = 0.5 𝑁0 :
0.5𝑁0
ln
= −𝜆𝑇1/2
𝑁0
ln 0.5 = −𝜆𝑇1/2
−0.693 = −𝜆𝑇1/2
𝑇1/2
0.693
=
𝜆
Question 9
What is the half life, in years, of a source of Carbon14, if it has a decay constant of 3.92 × 10−12 s-1?
𝑇1/2
0.693
=
𝜆
𝑇1/2
0.693
=
3.92 × 10−12
𝑇1/2 = 1.7679 × 1011 𝑠
Divide by (365 × 24 × 60 × 60):
𝑇1/2 = 5606 𝑦𝑒𝑎𝑟𝑠
Label the following:
Number of Nuclei
N0
½ N0
T1/2
0.693
𝜆=
𝑇1/2
Uses of Radioactivity
Uses of radioactivity
- Each of you will have two lessons (plus prep) to prepare a
7 minute presentation on one of:
•
•
•
•
•
Carbon dating
Argon dating
Radioactive tracers (Medicine)
Industry
Other
- You also need to prepare 1 side of A4 with all of the
important information as a handout for the other
students in your class (and me!)
- You can use books, the internet etc. to research
- Feel free to be creative! Add a little quiz or fun
competition and question the class, or ask for
volunteers...!
Some uses…
These materials have a variety of uses and a selection of these are listed
below.
(a)
dating geological specimens, using uranium, rubidium or bismuth;
(b)
dating archaeological specimens, using carbon 14
(c)
paper or plastic thickness measurement using beta radiation
(d)
treatment of tumours;
(e)
sterilisation of foods;
(f)
nuclear pacemakers for the heart;
(g)
liquid flow measurement;
(h)
tracing sewage or silt in the sea or rivers;
(i)
checking blood circulation and blood volume;
(j)
atomic lights using krypton 85;
(k)
checking the silver content of coins;
(I)
radiographs of castings and teeth;
(m)
testing for leaks in pipes;
(n)
tracing phosphate fertilisers using phosphorus 32
(o)
smoke alarms
(p)
sterilisation of insects for pest control.
N-Z diagrams and nuclear radius
Recap Question!
A radioactive source starts with 5000 Bq activity at t=0, but
has 2000 Bq at time t=10s. Find the decay constant:
𝐴 = 𝐴0 𝑒 −𝜆𝑡
𝐴
= 𝑒 −𝜆𝑡
𝐴0
𝐴
ln
= −𝜆𝑡
𝐴0
𝐴
ln
𝐴0
𝜆=
−𝑡
𝜆 = 0.0916 s-1
2000
ln
5000
=
−10
9.8 More about decay modes
How can we tell if a particular
isotope of a nucleus is stable?
For atomic numbers Z up to
20, there are roughly the
same number of
protons/neutrons:
Z~N
For Z > 20, there are always
more neutrons:
N>Z
How could you use this graph to
determine which isotopes emit 
radiation ?
Segrè plot
Using the graph
Neutron
number
Why are proton rich
nuclei unstable?
n
p + e- + n
A
The strong nuclear force
is insufficient to
overcome coulombic
repulsion
+
B
p
n + e+ + n
How would the arrows
be placed for alpha
decay?
Proton number
Radioactive decay process
 decay
Z
N
Z–2
N–2
proton number Z

2 fewer protons
2 fewer neutrons
– decay
–
Z
N
Z+1
N–1
n
proton number Z
1 more proton
1 less neutron
+ decay
+
Z–1
N+1
Z
N
proton number Z
n
1 less proton
1 more neutron
Neutron number
(N)
This can be summarised as
N+1, Z-1
+
N, Z

N-2, Z-2
N-1, Z+1
Proton number (Z)
Task
Draw the NZ diagram for radon decay:
222Ra-86 (,,,,,,,)
What does it form…?
Lead-206!
Stable and unstable nuclei: balance of numbers of protons and neutrons
stable
alpha decay
150
beta decay
electron capture
positron emission
fission
100
N=Z
50
0
0
20
40
60
proton number Z
80
100
N+1
n
Z
N
What about gamma decay?
proton number Z
1 less proton
1 more neutron
decay
What is gamma?
Where does it come
from?
Z
N
proton number Z
Recall photon absorption by atomsit’s pretty much the same idea, but
this time we are talking about the
NUCLEUS being in excited energy
states!

same protons
and neutrons
Energy levels in nuclei
Nuclei also have discrete energy levels.
Following decay, the nucleus is often left in an excited state (we call this a
“metastable” state)!
The nucleus will rearrange itself to form the lowest, and most stable
configuration.
Energy is released as a high energy wave – a  photon
Technetium generators
Research and write about why Technetium-99 might be used in hospitals.
Comment on:
- How it’s produced
- The type of radiation emitted
- The Half-lives
De Broglie
Why can’t we use light to look at
atoms?
Light is limited by its wavelength to
resolving objects about 1 m across.
Below this length diffraction becomes
important.
Waves will not travel through a gap
less than a wavelength.
Why can we use electrons ?
Because they have wave properties and their
de Broglie wavelength is very small, but not
small enough at normal energies
To get the resolutions required to look at
the nucleus, we need de Broglie
wavelengths of 10-15 m.
What p.d must an electron be
accelerated by to achieve this
wavelength?
100 MegaVolts!
If we use more massive particles,
we can obtain much shorter de
Broglie wavelengths, hence
more resolution.
What is the problem with this?
Nuclei bombarded with high energy
particles tend to break up.
It has been described as finding out how a
watch works by smashing it with another
watch, and guessing how the pieces fit
together…
Electron scattering
A more accurate estimate of the
nuclear radius has been determined
by the use of a technique called
electron scattering.
In terms of the four fundamental
forces, why are electrons more useful
than alpha particles in the scattering
experiments used to probe the
nucleus?
The electrons interact with the nucleus entirely by the electromagnetic
interaction whereas the alpha particles interact by the strong nuclear
interaction, which is not well understood
What’s going on (E)
Medium energy
electron
Quarks move
rapidly inside
of the proton
Electron
scattered
through a
larger angle
High energy
electron
Collision between the
electron and one quark
Nuclear Radius (R)
R = r0 A1/3
Radius of the nuclei, R is measured in metres (m)
Constant, r0 is 1.05 fm (1.05 x 10-15 m)
Mass number, A (the number of nucleons) is unitless
Nuclear Radius (R)
R = r0 A1/3
What would we get if we plotted ln(R) Vs ln(A)?
ln(R)
Intercept = ln(r0)
ln(A)
Nuclear Radius (R)
R = r0 A1/3
What would we get if we plotted R Vs A1/3?
R
A1/3
Nuclear Radius (R)
R = r0 A1/3
What would we get if we plotted R3 Vs A?
R3
A
Nuclear density
What does the tailing
off of the graph
suggest?
That the nucleus does
not have a hard edge
On this scale, the nearest
star would be a little over
10,000 miles away
Finding the density
What is the formula for density,  ?
How do you find the
volume of a sphere?
So:
V 
Mass of a nucleus:

V
m
V
4
R 3
3
4
4
 ( r0 A1/ 3 ) 3  r0 3 A
3
3
m  A mp
Remember:
R = r0 A1/3 !
Finding the density
Show that the nuclear density is:
-
Constant
Independent of the radius
𝜌=
1.67 × 10−27
4
𝜋(1.05 × 10−15 )3
3
𝜌 = 3.4 × 1017 𝑘𝑔𝑚−3
𝑚
𝜌=
𝑉
𝐴𝑚𝑝
𝜌=
4 3
𝜋𝑟0 𝐴
3
𝑚𝑝
𝜌=
4 3
𝜋𝑟
3 0
Question
(a) What is the nuclear radius of an iron-56 atom?
(b) Would the radius be any different to a cobalt-56
nucleus?
(a) 𝑹 = 𝒓𝟎A1/3
𝑹 = (𝟏. 𝟎𝟓 × 𝟏𝟎−𝟏𝟓 ) × 𝟓𝟔1/3
𝐑 = 𝟒. 𝟎𝟐 × 𝟏𝟎−𝟏𝟓 𝒎
(b) No- they have the same number of nucleons!