CHEMISTRY 1000
Nuclear Chemistry
Radioactivity and Radiation

Nuclear reactions result in changing the nuclei of atoms. These
reactions are accompanied by emission of ionizing radiation
(which has enough energy to excite electrons out of molecules,
‘ionizing’ them). There are three main types of ionizing radiation:


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alpha rays (): helium nuclei (2 protons + 2 neutrons)
beta rays (): electrons
gamma rays (): high energy photons (higher energy than x-rays)
which have no mass and no charge
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Radioactivity and Radiation
•
•
•
•
-particles can be stopped by paper.
-particles require at least a cm of lead (Pb).
-particles require at least 10 cm of lead (Pb).
Neutrinos: zero charged particles even smaller
than electrons.
Energy:  >  > 
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Measuring Radiation
rad = radiation absorbed dose
rem = radiation equivatlent for man
Q = RBE (relative biological effectiveness)
Sv = Gy x Q
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Effects of Radiation Exposure (long term)

Natural and Artificial Sources of Radiation.
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Effects of Radiation (Short Term)
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Calculating Radiation Dosage

Example: Calculate the radiation dosage (in Sieverts) for a person
weighing 68 kg that is exposed to 3.5×108 particles of alpha radiation.
Assume that 89% of the radiation is absorbed and each alpha particle
has an energy of 6.2×10-13 J, and that the RBE or Q of alpha particles is
15.
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Short Term Exposure vs Long Term Exposure
• Safe dose for single exposure is much higher
than safe dose for long term exposure
• Annual exposure to background radiation in
Canada depends on location but typically
about 3 mSv (=3000 µSv = 300 mrem)
• Legal limits to radiation exposure at work (50
mSv/year, 100 mSv over five year)
• Legal doses: LD50 for a single exposure 4 Sv
LD50 for ongoing exposure is …
http://www.hc-sc.gc.ca/hl-vs/iyh-vsv/environ/expos-eng.php
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Nuclear Medicine: Imaging
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mass number (A)
Balancing Nuclear Reactions

atomic number (Z)
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6
C
In any nuclear reaction, two things are conserved:
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The sum of the mass numbers of the products is equal to the sum
of the mass numbers of the reactants.
The sum of the atomic numbers of the products is equal to the sum
of the atomic numbers of the reactants.
The “atomic number” for an electron () is considered to be -1.

The exact masses of products and reactants are not the same.
The small mass difference between mass of products and
reactants results in release of energy (E = mc2) and the law
of conservation of energy still holds. (The law of conservation
of mass is a special case of the law of conservation of energy.)
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mass number (A)
Balancing Nuclear Reactions

atomic number (Z)
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6
C
Balance the following nuclear reactions.
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Be
4
0
-1 e
235
U
92
231
Th
90
218
At
85
4

2
206
Tl
81
236
92 U
0
-1 e
141
56 Ba
+ 3 10 n
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Classes of Nuclear Reactions
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There are seven classes of nuclear reactions:
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Alpha emission
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Beta emission
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Positron emission
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Electron capture
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Fusion
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Fission
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Bombardment (to make transuranium elements)
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Classes of Nuclear Reactions
reactants
products*
ΔZ
spontaneous?
alpha emission
1 nucleus
1 nucleus + 1 alpha particle
-2
yes
beta emission
1 nucleus
1 nucleus + 1 electron
+1
yes
positron emission
1 nucleus
1 nucleus + 1 positron**
-1
yes
electron capture
1 nucleus + 1 electron
1 nucleus
-1
yes
fission
1 nucleus
2 nuclei + neutron(s)
varies
no
fusion
2 light nuclei
1 nucleus + neutron(s)
varies
sometimes
2 heavy nuclei
1 nucleus + neutron(s)
varies
no
bombardment
Most nuclear reactions also emit electromagnetic radiation. Emitting an  or  particle leaves
the nucleus in an excited state so it emits a photon as it returns to the nuclear ground state.
The energy of the photon is specific to the nuclear reaction.
** As antimatter, positrons are not directly observable. A positron is annihilated as soon as it
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collides with an electron, releasing  radiation (a high energy photon).
*
“nuclide” = a specific type of nucleus (i.e. containing a specific #protons and #neutrons)
Classes of Nuclear Reactions

An unstable nuclide undergoes spontaneous nuclear reaction to
form a more stable nuclide. If this product is also unstable, it
undergoes another nuclear reaction (and another and another,
etc. until a stable nuclide is reached). Such a series of alphaand beta-emissions is called a radioactive decay series:
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Classes of Nuclear Reactions

Some classes of nuclear reaction, on the other hand, will never
occur spontaneously. Instead, they must be induced (often by
hitting the nucleus with a neutron to generate a highly unstable
nucleus which will then undergo the desired nuclear reaction).
This is true of fission and bombardment:
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Why Do Nuclear Reactions Occur?

What factors affect stability of a particular nuclide?
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A nucleus consists of protons and neutrons held together by
nuclear binding energy.
At the same time, there is electrostatic repulsion between the
positively-charged protons. If this repulsion is too great, the
nucleus will be unstable.
Neutrons lessen this repulsion by increasing the distance between
protons; however, neutrons are inherently less stable than protons.
Excess neutrons will decompose into proton/electron pairs.
It is therefore possible to make a few generalizations:
 Nuclides containing more protons need more neutrons (to
keep the protons apart).
 Nuclides containing fewer protons need fewer neutrons (to
maximize stability).
 There is a maximum number of protons beyond which the
nuclear binding energy cannot hold the nuclide together stably
(because the electrostatic repulsion is too great).
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Why Do Nuclear Reactions Occur?

The number of stable nuclides is relatively small. Plotting
#protons (Z) vs. #neutrons (N) for all nuclides that have been
made/found gives a narrow band of stable nuclides (black dots)
surrounded by a wider band of unstable nuclides (red dots).
The stable nuclides form the band of stability.

Nuclides farthest from the band of stability are
least stable, decaying fastest.

Heavy nuclides decay faster than light ones.
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N-to-Z ratio in stable nuclides is predictable:
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If Z = 1-20 (H to Ca), N  Z is ideal
If Z = 20-83 (Sc to Bi), N > Z up to N  1.5 Z
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If Z  84 (Po and larger), no stable nuclides exist
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Even values for Z & N are conducive to stability.
Almost 60% of stable nuclides have both even.
Less than 2% of stable nuclides have both odd!
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Why Do Nuclear Reactions Occur?
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The type of nuclear reaction which a nuclide is most likely to
undergo can be predicted from its N-to-Z ratio.
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A nucleus which has “too many neutrons” (i.e. N/Z is too high) will
tend to undergo beta emission. How does this improve N/Z?
A small nucleus which has “too many protons” (i.e. N/Z is too low)
will tend to undergo either positron emission or electron capture.
How does this improve N/Z?
A large nucleus which has “too many protons” (i.e. N/Z is too low)
will tend to undergo alpha emission. How does this improve N/Z?
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Nuclear Binding Energy

When nucleons (protons and neutrons) come together to make
a nucleus, energy is released. This energy is referred to as
nuclear binding energy (E) and a nuclide’s nuclear binding
energy can be calculated using Einstein’s famous equation:
The nuclear binding energy for any nuclide can thus be
calculated by comparing its mass to the total mass of the
protons and neutrons it contains. You may have already
noticed that atomic masses are not exactly equal to the sum of
the masses of the protons, neutrons and electrons in the atom!

In order for a nuclide to be stable, its nuclear binding energy
must be greater than the electrostatic repulsion between its
protons.
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Nuclear Binding Energy
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Since they release more energy upon formation, nuclides with
greater nuclear binding energies would at first seem to be more
stable; however, we must also factor in the number of
nucleons brought together. Otherwise, larger nuclides appear
to be excessively stable are simply because they contain more
nucleons.
So, a more useful quantity to calculate is the nuclear binding
energy per nucleon (Eb):
Eb 
E
A
where A = mass number = #nucleons = Z + N

Nuclides with larger Eb values are more stable.
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Nuclear Binding Energy

Mproton = 1.0072765 g/mol
Mneutron = 1.0086649 g/mol
Melectron = 0.0005486 g/mol
Calculate Eb for the helium isotopes: 3He (3.016029310 g/mol)
and 4He (4.002603250 g/mol). Which isotope is more stable?
For this type of calculation, ALWAYS use the mass of the specific isotope or nuclide.
NEVER use the average atomic mass listed on the periodic table
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Nuclear Binding Energy
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4He
is one of the most stable nuclide. When Eb is plotted as a
function of A, the most stable nuclide is found to be 56Fe:
This plot also shows which nuclides can undergo fusion
(increasing Eb by increasing A) and which nuclides can undergo
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fission (increasing Eb by decreasing A).
Nuclear Binding Energy
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Since a nuclear reaction involves conversion of one (or more)
nucleus to another, it can be modeled as destruction of the
original nucleus followed by creation of a new nucleus:
So, we can calculate the energy released by any nuclear reaction
as long as we know the masses of the nuclides involved.
e.g. A neutron (1n, 1.0087 g/mol) strikes 235U (235.0439 g/mol)
to give 138Xe (137.908 g/mol), 95Sr (94.913 g/mol) and 3 1n.
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Rates of Radioactive Decay
Activity (A) = Disintegrations/time = (k)(N)
where N is the number of radioactive atoms
k is decay constant (in s-1) and is characteristic of a
particular decay.
Activity can be measured using a Geiger counter or
scintillation counter
If there are N1 atoms before
decay and N2 atoms after decay,
then the number of
disintegrations ΔN = N2-N1
during a time change of
Δt = t2 - t1
So A = -ΔN/Δt = (k)(N)
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Can We Find the Decay Constant by Graphing?
From A = -ΔN/Δt = kN, if we can measure A and N in the
lab, we can graph A vs. N to find k, as A = kN is a linear
equation like y = ax. The slope of the line A vs. N would give
k.
What does this graph look like?
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Can We Find the Decay Constant by Graphing?
However, even if we can measure Δt and N in the lab, a
graph of N vs. Δt would not be linear and therefore not
useful in finding k, as N = (-ΔN/k)Δt is not a linear equation
like y = ax, but a non-linear equation like y = a/x.
What does this graph look like?
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Fortunately, Radioactive Decay
is a first-order reaction The rate of the reaction
only depends on the
“reactant” concentration.
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What Is the Half-Life of a Radioactive Decay?
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Finding Half-Life from a Graph
After each successive half-life, one half of the original amount
remains.
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Radiocarbon Dating
Willard Libby (1908-1980)
Libby received the 1960 Nobel
Prize in chemistry for developing
carbon-14 dating techniques. He
is shown here with the apparatus
he used. Carbon-14 dating is
widely used in fields such as
anthropology and archeology.
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Radiocarbon Dating
Radioactive 14C is formed in the upper atmosphere by
nuclear reactions initiated by neutrons in cosmic
radiation:
14N + 1 n  14C + 1H
0
The 14C is oxidized to CO2, which circulates through
the biosphere.
When a plant dies, the 14C is not replenished.
But the 14C continues to decay with t1/2 = 5730 years.
Activity of a sample can be used to date the sample.
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Is There a Limit for Carbon-14 Dating?
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Transuranium Elements & Glenn Seaborg
Sg
106
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Nuclear Fission
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Nuclear Fission
Fission chain reaction has three general steps:
Initiation:
Reaction of a single atom starts the chain (e.g.,
235U + neutron)
Propagation:
236U fission releases neutrons that initiate other
fissions
Termination:
Consumption of the fissionable material is
completed
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Nuclear Fission & Lise Meitner
109Mt
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Nuclear Fission & Power
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Currently about 103 nuclear power plants in the
U.S. and about 435 worldwide.
17% of the world’s energy comes from nuclear
reactions.
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