NUCLEAR CHEMISTRY
NUCLEONS – The particles found in the nucleus
Protons (+)
Neutrons (0)
ATOMIC NUMBER (Z) – The number of protons in the nucleus, also equal
to the charge of the nucleus
MASS NUMBER (A) – The number of nucleons in the nucleus, or protons
plus neutrons in the nucleus
2F-1 (of 15)
NUCLIDE – An atom with a specific number of protons and neutrons
A  196
Hg
Z 
80
Protons:
80
Neutrons: 196 - 80 = 116
ISOTOPES – A set of nuclides with the same number of protons
196
Hg
80
and
2F-2 (of 15)
198
Hg
80
are isotopes
NUCLEAR REACTIONS
Reactions that produce new atoms
TRANSMUTATION – When an atom of one element is changed into an atom
of another element
14
N
7
+
4
He
2
→
17
O
8
+
1
H
1
Artificial elements are made by bombarding large nuclei with smaller ones
238
U
92
+
2
H
1
→
238
Np
93
+ 2 01n
In all nuclear reactions (1) the mass number is conserved and (2) atomic
number (or charge) is conserved
2F-3 (of 15)
STABILITY SERIES
STABLE NUCLIDES (STABLE ISOTOPES) – Atoms with nuclei that last
forever
RADIOACTIVE NUCLIDES (RADIOISOTOPES) – Atoms with nuclei that
eventually break down to more stable nuclei
Nuclides are stable when their nuclei have enough neutrons to minimize
proton-proton repulsion
(a) For Z < 20
Stable nuclei have n:p ratio of 1:1
(b) For Z > 20
As Z increases, stable nuclei have n:p ratio that increases from 1:1 to
eventually 1.5:1
2F-4 (of 15)
Stable 16O atom:
8 n, 8 p
(1:1 ratio)
Stable 200Hg atom:
120 n, 80 p
1.5:1 ratio
Nuclides to the left of the line of stability are unstable because they are
neutron poor
Nuclides to the right of the line of stability are unstable because they are
neutron rich
Nuclides beyond the line of stability (with Z > 83) are unstable because
they have too many total protons
2F-5 (of 15)
There are 284 known stable nuclides
Neutrons
Protons
Even
Odd
Even
166
53
Odd
57
8
Most of the stable nuclides have even numbers of protons and neutrons
2F-6 (of 15)
NUCLEAR DECAY – The process in which a radioactive nuclide turns
into a more stable nuclide
The type of decay depends on whether the radioactive nuclide has too
many total protons, if it is neutron rich, or if it is neutron poor
2F-7 (of 15)
(1) ALPHA DECAY (α) – The release of a helium-4 nucleus (4He2+) from a
radioactive nucleus to become more stable
α’s are emitted from radioisotopes beyond the line of stability, those
with too many total protons (Z > 83 or A > 200)
238
U
92
→
4
α
2
+
234
Th
90
A and Z are always conserved in nuclear changes
Alpha particles can be stopped by the outermost layer of skin
2F-8 (of 15)
(2) BETA MINUS DECAY (β-) – The release of an electron from a radioactive
nucleus to become more stable
β-’s are emitted from radioisotopes that are to the right of the line of
stability, those that are neutron rich
Essentially a neutron decays into a proton and an electron
14
6
C →
0
-1
β- +
14
7
N
Beta particles penetrate about 1 cm into the body
2F-9 (of 15)
(3) ELECTRON CAPTURE (EC) – An electron is captured by the nucleus to
become more stable
EC occurs in radioisotopes to the left of the line of stability, those that
are neutron poor
Essentially an electron and a proton turn into a neutron
7
4
Be +
2F-10 (of 15)
0
-1
e- →
7
3
Li
(4) POSITRON DECAY (β+) – The release of an electron with a positive
charge from a nucleus to become more stable
β+’s are just like electrons, but with a positive charge
An electron is matter, but a β+ is ANTIMATTER
When a β+ and β- meet, they are ANNIHILATED, meaning all of their
mass is converted into energy
A β+/β- annihilation forms 2 equal energy EM radiation photons
2F-11 (of 15)
(4) POSITRON DECAY (β+) – The release of an electron with a positive
charge from a nucleus to become more stable
β+’s are emitted from radioisotopes to the left of the line of stability,
those that are neutron poor
Essentially a proton decays into a neutron and an antimatter electron
11
6
C →
2F-12 (of 15)
0
1
β+ +
11
5
B
(5) GAMMA DECAY (γ) – The release of any high energy photon of
electromagnetic radiation
γ’s are emitted along with other forms of decay, or when an excited
nucleus releases energy
40
K
19
163m
Ho
67
→
→
0
-1
β- +
0
0
γ +
40
Ca
20
163
67
+
0
γ
0
Ho
Gamma rays are deeply penetrating
2F-13 (of 15)
2F-14 (of 15)
(6) SPONTANEOUS FISSION – When a large nucleus (Z > 80) breaks into
two, approximately equal halves
Several neutrons, and lots of energy are released when nuclei fission
239
U
92
→
116
Ru
44
+
120
Cd
48
+ 3 10n
239
U
92
→
118
Rh
45
+
119
Ag
47
+ 2 10n
Daughter Products
usually very radioactive, and always different
2F-15 (of 15)
THE RATE OF NUCLEAR DECAY
Each radioisotope undergoes nuclear decay at its own unique rate
HALF-LIFE (t1/2) – The time required for half of the radioisotopes in a
sample to decay
The shorter the half-life, the more unstable the radioisotope
Half-life for 125I = 60 days
At
0 days: 16 125I atoms
60 days:
8 125I atoms
At 120 days:
4 125I atoms
At 180 days:
2 125I atoms
At 240 days:
1 125I atom
At
2G-1 (of 17)
Half-lives range from
1 x 10-21 seconds for 18Na
5 x 1015 years for 142Ce
Common half-lives
5,730 years for 14C
4.5 x 109 years for 238U
2G-2 (of 17)
THE DECAY EQUATION
n = n0e-kt
n0 =
k =
t =
n =
at time 0, number of atoms of a radioisotope (or g or disintegrations/time)
decay constant of a radioisotope (disintegrations atom-1 time-1)
time of decay
at time t, number of atoms of a radioisotope (or g or disintegrations/time)
2G-3 (of 17)
Half-life (t1/2) is the time needed so that ½ of n0 disintegrates
n = n0e-kt
n0 = n0e-kt1/2
___
2
1 = e-kt1/2
___
2
ln (1/2) = -kt1/2
ln 2 = kt1/2
ln 2 = t1/2
_____
k
2G-4 (of 17)
or
ln 2 = k
_____
t1/2
THE DECAY EQUATION
n = n0e-kt
2G-5 (of 17)
n = n0e- (ln2/t1/2)t
Calculate the mass of 110Ag remaining after 2.00 minutes if you start with
1.00 g 110Ag and its half-life is 24 seconds.
n = n0e-(ln2/t1/2)t
n and no can be anything proportional to the number of the radioactive
atoms:
(1) grams, (2) moles, (3) disintegrations per time, (4) percentages, or of
course (5) atoms
= (1.00 g)e-(ln2/24 s)(120. s)
= 0.031 g
2G-6 (of 17)
Starting with 2.00 g of a radioisotope, after 1.00 hour only 0.63 g remain.
Calculate the half-life.
n = n0e-(ln2/t1/2)t
n = e-(ln2/t1/2)t
___
n0
ln (n/n0) = -(ln2/t1/2)t
t1/2 =
-(ln2)t
__________
ln (n/n0)
2G-7 (of 17)
=
(ln2)t
__________
ln (n0/n)
=
(ln2)(1.00 h)
_____________________
ln (2.00 g/0.63 g)
= 0.60 h
CARBON DATING
In the atmosphere
14
N
7
+
1
n
0
→
14
C
6
14
6C
+ O2
→
14
CO2
6
+
1
H
1
The carbon in all living organisms
has the same percentage of 14C
that the atmosphere has
15.3 dist. min-1 g-1 of carbon
When an organism dies, it stops
taking in 14C, so the percentage
starts dropping
2G-8 (of 17)
An axe with an elk antler sleve produces 4.8
cpm g-1 of carbon. How old is the axe?
n = n0e-(ln2/t1/2)t
n = e-(ln2/t1/2)t
___
n0
ln (n/n0) = -(ln2/t1/2)t
t1/2 ln (n0/n) = t
______________
ln 2
2G-9 (of 17)
= (5,730 y) ln (15.3 cpm g-1/4.8 cpm g-1)
_______________________________________________
ln 2
=
9,600 y
Much older objects can be dated with radioisotopes of longer half-lives
238U
decays to 206Pb, so a material containing uranium can be dated by
measuring the amount of 206Pb compared to 238U
2G-10 (of 17)
A rock weighing 4.267 g contains 1.023 g 238U and 0.112 g 206Pb. Calculate
the age of the rock.
t1/2 ln (n0/n) = t = (4.5 x 109 y) ln (1.152 g/1.023 g)
______________
_______________________________________
ln 2
= 7.7 x 108 y
ln 2
t1/2 = 4.5 x 109 y
n = 1.023 g
n0 = the original mass of 238U
0.112 g 206Pb x mol 206Pb x 1 mol 238U
______________
______________
206 g 206Pb
1 mol 206Pb
= 0.129 g + 1.023 g = 1.152 g
2G-11 (of 17)
x 238 g 238U
_____________
mol 238U
STABILITY OF NUCLEI
Mass of proton + electron :
Mass of neutron
:
1.007825 amu
1.008665 amu
Calculate the mass of a 23Na atom.
11 p+ + e12 n
11 x 1.007825 amu
12 x 1.008665 amu
=
=
11.086075 amu
12.103980 amu
=
23.190055 amu
Mass spectrometer data
Mass 23Na
2G-12 (of 17)
:
22.989773 amu
BINDING ENERGY – The mass of an atom that has been converted into
energy to hold the nucleus together
Mass loss of a 23Na atom:
23.190055 amu – 22.989773 amu = 0.200282 amu
Through E = mc2 mass units can be converted into energy units
1.000 amu = 1.492 x 10-10 J
= 9.315 x 108 eV
= 931.5 MeV
2G-13 (of 17)
(Joule)
(Electron Volt)
(Million Electron Volt)
0.200282 amu x 931.5 MeV
______________
= 186.6 MeV
1.000 amu
This is the BINDING ENERGY of the 23Na nucleus
The stability of a nucleus is measured by its BINDING ENERGY PER
NUCLEON
186.6 MeV
________________
23 nucleons
2G-14 (of 17)
=
8.113 MeV/nucleon
Calculate the binding energy per nucleon for 56Fe if it has a mass of
55.934930 amu.
26 p+ + e30 n
26 x 1.007825 amu
30 x 1.008665 amu
=
=
26.203450 amu
30.259950 amu
=
56.463400 amu
56.463400 amu – 55.934930 amu =
0.528470 amu
0.528470 amu x 931.5 MeV x
2G-15 (of 17)
1
______________
_______________
1.000 amu
56 nucleons
=
8.791 MeV/nucleon
56Fe
is the most stable atom
When large atoms break down they release energy
When small atoms combine they release energy
2G-16 (of 17)
FUSION – The combining of small nuclei to produce large nuclei
Fusion occurs in stars
4 11 H →
4
2
He
Very high temperatures or pressure are needed to overcome the
repulsion of the positive hydrogen nuclei
Fusion releases much more energy than fission
Stars can fuse atoms to create even atomic numbered elements all
the way up to 56Fe
2G-17 (of 17)
NUCLEAR REACTORS
Nuclear reactions release over 100 times
more energy than chemical reactions
235U
is used as a fuel
235
U
92
236U
+
1
0
n →
236
U
92
decays by spontaneous fission
CHAIN REACTION – When at least one
neutron per fission produces a new 236U
2G’-1 (of 4)
Not enough
neutrons are
captured for a
chain reaction
Enough neutrons
are captured to
just maintain a
chain reaction
So many neutrons
are captured the
chain reaction is
an explosion
CRITICAL MASS – The minimum amount of 235U needed to support a chain
reaction
2G’-2 (of 4)
Water – Acts as a MODERATOR to
slow down the neutrons, as a
COOLANT to keep the reactor
core from overheating, and as
PROTECTION because it absorbs
radiation
Cd or B Control Rods – Absorb
neutrons to control the rate of
the chain reaction
Fuel Elements – Metal casings
containing 235U
Reactor Core
2G’-3 (of 4)
San Onofre Nuclear Generating
Station
Heat from the nuclear fission
boils water, and steam turns a
turbine, which produces
electricity
Used up full elements contain
radioactive daughter products,
which must be disposed of
safely
2G’-4 (of 4)