Chapter 23 – Nuclear Chemistry
Nuclear chemistry involves changing the nucleus of an atom.
Frequently, this change is accompanied by emission of ionizing
radiation (so called because it has enough energy to excite
electrons out of molecules, ‘ionizing’ them).
There are four main types of ionizing radiation:
1. alpha rays: helium nuclei (2 protons + 2 neutrons)
2. positron rays: positrons (the antimatter counterparts to
electrons; same mass but charge is +1)
3. beta rays: electrons
4. gamma rays: high energy photons (E = hν; ν ≥ 1020 Hz;
higher energy than x-rays)
radiation
alpha
symbol
4
2α
or
4
2 He
charge
mass
penetrating
(per particle)
power
+2
6.65 × 10-24 g
lowest
positron
0
β
1
or 0 e
+1
9.11 × 10-28 g
medium
beta
0
β
-1
or 0 e
-1
9.11 × 10-28 g
medium
0
0
highest
gamma
1
-1
0γ
0
Nuclear Reactions
Unlike all other chemical reactions, a nuclear reaction allows an
atom to change from one element to another. The law of
conservation of mass is still upheld, though, and the total
number of nucleons (protons and neutrons) does not change.
In Chapter 2, we described atoms using their atomic and mass
numbers:
mass number (A)
12
6
atomic number (Z)
C
In a nuclear reaction, the total mass numbers of reactants and
products are equal. Similarly, the total atomic numbers of
reactants and products are equal. This is why it is important to
include the mass and atomic numbers of the rays emitted.
Σ Areactants
=
Σ Aproducts
Σ Zreactants
and
=
Σ Zproducts
Balance the following nuclear reactions:
7
4
Be +
0
-1 e
235
92 U
231
90 Th
218
85
+
At +
206
81 Tl
236
92 U
0
-1
+
141
56 Ba
+
e
4
2
α
+ 3 10 n
There are 7 classes of nuclear reaction:
1. alpha emission: A nucleus emits an alpha particle.
2. beta emission: A nucleus emits an electron. Essentially, a
neutron decomposes to a proton and an electron then the
nucleus emits the electron.
3. positron emission: A nucleus emits a positron. Essentially,
a proton decomposes to a neutron and a positron then the
nucleus emits the positron.
4. electron capture: An electron (from the atom’s 1s orbital) is
incorporated into the nucleus.
5. nuclear fission: A nucleus breaks into two smaller nuclei.
6. nuclear fusion: Two light nuclei join to make one larger
nucleus.
7. nuclear transmutation: Two heavy nuclei join to make one
larger nucleus of an artificial element.
reactants
alpha emission
1 nucleus
beta emission
1 nucleus
positron
emission
electron
capture
1 nucleus
1 nucleus +
electron
products*
1 nucleus +
alpha particle
1 nucleus +
electron
1 nucleus +
positron
∆Z
spontaneous?
-2
yes
+1
yes
-1
yes
1 nucleus
-1
yes
2 nuclei +
varies
no
neutron(s)
2 light
1 nucleus +
varies sometimes
nuclear fusion
nuclei
neutron(s)
nuclear
2 heavy
1 nucleus +
varies
no
transmutation
nuclei
neutron(s)
*
Most nuclear reactions also emit gamma rays (γ). Emitting a
particle (α, β or positron) leaves the nucleus in an excited state
so it emits a gamma ray to return to the nuclear ground state.
The energy of the gamma ray is specific to the nuclear reaction.
nuclear fission
1 nucleus
An unstable nucleus undergoes spontaneous nuclear reaction to
form a more stable nucleus. If this product is also unstable, it
undergoes another nuclear reaction (and another and another,
etc. until a stable nucleus is reached). Such a series of alphaand beta-emissions is called a radioactive decay series.
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 transmutation.
Stability of Atomic Nuclei
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. Neutrons
lessen this repulsion by increasing the distance between protons.
These three points allow us to make a couple of generalizations:
1. Atoms with more protons need more neutrons.
2. There is a maximum number of protons beyond which the
nuclear binding energy cannot hold the nucleus together
(because the electrostatic repulsion is too great).
The number of stable isotopes is relatively small.
If we plot the allowed
isotopes for the various
elements on a graph of the
number of protons versus the
number of neutrons, we
obtain a narrow band of
stable isotopes (in black)
surrounded by a wider band
of unstable isotopes (in red).
The stable isotopes form the
band of stability.
The isotopes farthest from the
band of stability are the least
stable, decaying the fastest.
Heavy isotopes also decay
faster than light ones.
For Z = 1 to 20 (H to Ca), stable isotopes have N ≈ Z
For Z = 21 to 83 (Sc to Bi), stable isotopes have N > Z
For Z ≥ 84 (Po and up), there are no stable isotopes.
Unstable nuclei with ‘too many neutrons’ can approach the band
of stability by converting neutrons to protons as part of beta
emission.
Small unstable nuclei with ‘too many protons’ can approach the
band of stability by converting protons to neutrons as part of
either positron-emission or electron capture.
Large unstable nuclei with ‘too many protons’ tend to improve
their N : Z ratio via alpha emission. Nuclei larger than bismuth
also use alpha emission to reduce Z.
In order for a nucleus to be stable, the nuclear binding energy
must be higher than the electrostatic repulsion between protons.
Nuclear binding energy is defined as the energy required to
separate a nucleus into its component protons and neutrons.
We can calculate nuclear binding energy by comparing the mass
of a nucleus to the mass of the protons and neutrons forming it.
The mass of the complete nucleus is always lower, and the
“mass defect” is the source of the nuclear binding energy:
∆E = ∆mc2
where ∆E is total nuclear binding energy, ∆m is the mass defect
and c is the speed of light.
While nuclear masses are not widely tabulated, atomic masses
are. As such, we can obtain ∆m by subtracting the atomic mass
of an isotope from the combined masses of the protons, neutrons
and electrons:
∆m = (Z · mproton + Z · melectron + N · mneutron) – misotope
where Z is atomic number and N is the number of neutrons.
mproton = 1.0072765 g/mol
melectron = 0.0005486 g/mol
mneutron = 1.0086649 g/mol
Remember to use the mass of the isotope in question – NOT the
average atomic mass listed on the periodic table.
When comparing nuclear binding energies of different isotopes,
we are more interested in Eb, the nuclear binding energy per
nucleon:
Eb = ∆E = ∆mc2
A
A
where A is the mass number of the isotope.
e.g. Calculate nuclear binding energies (per atom and per
nucleon) for the helium isotopes: 3He (3.016029310 g/mol)
and 4He (4.002603250 g/mol). Which isotope would you
predict to be more stable?
Generally, nuclear binding energies (Eb) are 108 to 109 kJ/mol.
You may occasionally see binding energies listed in MeV:
1 MeV = 9.6485342 × 107 kJ/mol
The MeV is the preferred unit of the nuclear industry uses the
since values for Eb are therefore ~0 to 9 MeV.
The most stable nucleus is _____. Eb generally increases as
mass number approaches 56 from either direction (except that
4
He has an unusually high Eb). Isotopes with mass numbers
below ____ can undergo fusion to make a more stable nucleus.
Isotopes with mass numbers above ____ can undergo fission to
make more stable nuclei. Isotopes with mass numbers between
____ and ____ are generally stable and will undergo neither
fusion or fission.
Making Artificial Elements
Uranium (Z = 92) is the largest naturally occurring element. All
larger elements are synthetic – either byproducts of nuclear
reactions or deliberately made by nuclear transmutation.
The first recorded nuclear transmutation reaction was performed
by Rutherford in 1919. He found that bombarding atoms of
nitrogen with alpha particles produced oxygen:
More recently, Elements 113 (Uut, ununtrium) and 115 (Uup,
ununpentium) were added to the periodic table. In 2004, a
sample of 243Am was bombarded with atoms of 48Ca, giving one
atom of 287Uup and three of 288Uup:
Alpha emission then gave one atom of 283Uut and three atoms of
284
Uut (which was also unstable, decaying to Roentgenium, Rg):
Smaller synthetic elements (e.g. 239Pu) can be produced by
bombarding atoms with neutrons (instead of other atoms):
Neutron bombardment is an effective means to make elements
up to 101 (Mendelevium).
Rates of Nuclear Decay
The stability of an isotope is measured by its half-life, t1/2, (the
time required for half of a sample to decay).
Isotopes with long half-lives are more stable than those with
short half-lives, but this does not mean they are safer. An
isotope with a long half-life emits lower levels of radiation but
for a longer period of time (t1/2 for 238U is 4,470,000,000 years!)
while an isotope with a short half-life emits higher levels of
radiation for a short period of time before becoming ‘exhausted’.
Another two important factors to consider in assessing the
relative risk of radioactive isotopes are:
1. sample size, and
2. type of particle(s) emitted (and their energy!)
α
β (electrons or
positrons)
γ
energy
3.5 – 10 MeV
0.18 – 3.6 MeV
penetrating power
low
moderate
0.008 – 7.11 MeV
high
When we measure nuclear decay, we measure the number of
nuclei that disintegrate in a given period of time. This is termed
the activity (A) of a sample and is directly proportional to the
number of radioactive atoms (N) in the sample:
∆N
A =
= - kN
∆t
where k is the rate constant (aka decay constant).
By integrating this equation, we get a first-order rate equation:
ln
N
= - kt
N0
or
ln
A
= - kt
A0
where A0 and N0 are the initial activity and number of
radioactive atoms while A and N are the activity and number of
radioactive atoms after time ‘t’.
By definition, at t1/2, N = ½ N0. We can use this knowledge to
derive a relationship between k and t1/2:
The rate of radioactive decay has found practical application in
archaeology and paleontology where determining the age of
samples is important. Many different nuclei are used but the
most familiar process is “carbon dating” which uses 14C, the
naturally occurring radioactive isotope of carbon. At the
moment an organism dies, it has the same 12C : 13C : 14C ratio as
the atmosphere. From that moment on, the 14C decays slowly
while the 12C and 13C levels remain constant. Scientists can
therefore use the 12C : 13C : 14C ratio to estimate the age of an
item.
e.g. A table built from a tree cut down this year has a mass of
20 kg and emits 280,000 β particles per minute due to 14C
decay. The half-life of 14C is 5730 years.
(a) Calculate the decay constant for 14C.
(b) If an archaeologist discovers this table in 25,000 years,
what will be its activity (due to 14C decay)?
(c) If an archaeologist discovers this table and determines that
it emits 100,000 β particles per minute, in what year does
she make the discovery?
Measuring disintegrations per unit-time is useful for carbondating and other “how much isotope is present” techniques.
The SI unit for radioactivity is the becquerel, Bq:
1 Bq = 1 dps
You may also encounter the US unit, the curie, Ci:
1 Ci = 3.70 × 1010 dps
Medically, we are more interested in how much radiation is
absorbed by tissue than how much was originally produced.
The units for “radiation absorbed dose” are the rad (US) and the
gray, Gy (international):
1 rad = 0.01 J / kg
1 Gy = 1 J / kg
Different types of radiation do different amounts of damage to
tissue (even if the same amount of energy is absorbed), so there
are also units to describe the amount of biological damage done
by radiation. These units are the rem (US) and the sievert, Sv
(international).
It is estimated that the average North American is exposed to
between 130 and 190 mrem (millirems) of radiation in a year,
most of which is unavoidable ‘background radiation’. Single
exposures of less than 25 mrem are generally considered safe
and will not normally result in any observable effects (regular
exposures at this level may or may not be hazardous). On the
other hand, a single exposure of 200 mrem is fatal half the time.
When working with radiation, it is important to take precautions
to minimise exposure by wearing appropriate clothing,
following good lab practices, and using shields when necessary.
If it can be so dangerous, why do we use radiation therapy to
treat cancer?
Cancer cells grow and multiply faster than normal cells. Since
radiation damage generally affects cell growth, cancer cells are
damaged more easily than normal cells. The goal of radiation
therapy is to damage the cancer cells’ ability to grow/multiply,
thereby shrinking the tumour (or at least slowing its growth)
while minimizing damage to healthy tissue.
Chemotherapy also targets the cell growth/multiplication
mechanisms of cancer cells – but it uses toxic chemicals instead
of radiation to do the damage.
Important Concepts from Chapter 23
• types of ionizing radiation (α, β, γ and positrons)
• balancing nuclear reactions
• 7 classes of nuclear reactions
o α emission
o β emission
o positron emission
o electron capture
o nuclear fission
o nuclear fusion
o nuclear transmutation
• radioactive decay series
• nuclear binding energy (and nuclear stability)
• kinetics of nuclear decay
o activity
o half-life
o decay constant