The Nature of Radioactivity
John W. Moore
Conrad L. Stanitski
Peter C. Jurs
Henri Becquerel (1896):
• U salts emitted rays that “fog” a photographic plate.
• U metal was a stronger emitter.
http://academic.cengage.com/chemistry/moore
Marie and Pierre Curie:
• Isolated Po and Ra that did the same.
• Marie Curie called the phenomenon radioactivity.
Chapter 19
Nuclear Chemistry
Thomson and Rutherford:
• Studied the radiation, and found two types: α and β.
Stephen C. Foster • Mississippi State University
The Nature of Radioactivity
Name
Symbol
Charge
Mass (g)
Pen. Power*
alpha
4  4 He
2
2
+2
7 x 10-24
0.03 mm
-1
9 x 10-28
2 mm
0
0
beta
gamma
0 b 0e
-1
-1
0
0
g
100 mm
*Distance at which half the radiation has been stopped by water.
Villard:
• Discovered g radiation.
Nuclear Reactions
Rutherford & Soddy (1902)
“Radioactivity is the result of a natural change of a
radioactive isotope of one element into an isotope of a
different element”.
Ra
222
86 Rn
Radium-226
Radon-222
226
88
mass no. (A) 226
atomic no. (Z) 88
222
86
+
4
He
2
alpha particle
+
+
4
2
Note: A and Z must balance.
Alpha and Beta Particle Emission
Radioactive Series
Alpha – a nucleus ejects a helium nucleus:
A decay product
(daughter isotope) is
often unstable...
238
92
U
234
90 Th
+
4
He
2
Beta – a nucleus ejects an electron:
90
Sr
38
90
39Y
+
A radioactive series.
0
e
-1
How does a nucleus eject an e-? A series of steps, but
the net result is:
1
n
0
neutron
1
1p
proton
+
0
e
-1
The neutron number:
N=A-Z
electron
1
Other Types of Radioactive Decay
Other Types of Radioactive Decay
Positron emission
Positron = positive electron ( +10 e or +). Antimatter.
Electron capture (EC)
An inner-shell e- (K shell) is captured by the nucleus.
43
Sc
21
43
Ca
20
+
7
Be
4
0
e
+1
+
0
-1e
7
3
Li
Sometimes called K-capture.
Antimatter is annihilated by collision with matter:
 + + e-
2
Stability of Atomic Nuclei
Nuclear Equations
Radioactive iodine-131 is used to test thyroid function.
It undergoes beta decay to form a new element. Write
a balanced equation for the process.
Look up Z for I (Z = 53):
131
I
53
Add  (product):
131
I
53
0
e
-1
+
Calculate the Z and A for the new isotope:
131
I
53
0
e
-1
+
131
Xe
54
Element 54
The Band of Stability
Band of Stability & Type of Decay
Stable nuclei have N ≥ Z.
• Nuclei with Z < 20: N / Z ≈ 1.
• Nuclei with Z > 20: N / Z gradually increases.
• 209Bi (Z = 83) is the heaviest stable nucleus.
Elements with Z > 83
Most decay by alpha emission.
• Even-Z isotopes are more common than odd.
• Even-N isotopes are more common than odd.
 200 “even-even”; 120 “odd-even”; 4 “odd-odd”
Unstable isotopes decay so that the daughter will
enter the “peninsula of stability”.
Elements with Z<83
Use a periodic table
• Compare A with the element’s average atomic wt.
• Too heavy (excess n0):  emission (n0 → p+ + e-).
• Too light: + emission or e- capture (p+ → n0).
2
Band of Stability & Type of Decay
Binding Energy
Example
Predict how 28P will decay.
Atomic weight of P = 30.97
28P is too light. β+ decay.
A measure of the force holding a nucleus together.
Eb = −ΔEnucleus formation
E released when component p+ + n0 combine.
Example
How will 28Mg decay?
11
12
13
Na
Mg
Al
22.99
24.31
26.98
28Mg
14
15
16
Si
P
S
28.09
30.97
32.07
0
e
+1
28
15 P
+ 28
Si
14
is too heavy. β decay.
28
Mg
12
0
e
-1
+
28
Al
13
Einstein (special relativity): E = mc2
Eb = -ΔE = -(Δm) c2
with:
Δm = (mass nucleus) − (mass of p+ + n0)
c = speed of light = 2.99792458 x 108 ms-1
= 3.00 x 108 ms-1
Nuclear Binding Energy
Nuclear Binding Energy
Determine the binding energy and binding energy per
nucleon for 12C. The mass of 12C =12.00000 g/mol,
mn=1.00867 g/mol, and mp=1.00783 g/mol.
Determine the binding energy and binding energy per nucleon for 12C.
6 n 0:
6 x 1.00867
6 p+:
6 x 1.00783
Total mass nucleons
= 6.05202
= 6.04698
= 12.09900 g/mol
Δm = mass of nucleus – sum of nucleons
= 12.00000 – 12.09900 g/mol
= -0.09900 g/mol
Δm = −0.09900 g/mol = −9.900 x 10-5 kg/mol
ΔE = −9.900 x 10-5 kg/mol (2.998 x 108 m/s)2
ΔE = –8.898 x 1012 kg m2s-2 mol-1
Eb = −ΔE = +8.9 x 1012 J mol-1
(1J = 1kg m2 s-2)
Since 12C has 12 nucleons:
Eb/nucleon = (8.9 x 1012 / 12) = 7.4 x 1011 J mol-1
Nuclear Binding Energy
Rates of Disintegration Reactions
Eb/nucleon for stable isotopes:
Radioactive decay is 1st –order:
ln [X]t = −kt + ln [X]0
[X]0 = initial concentration of isotope X
[X]t = concentration of X after time t
k = rate constant.
Half life:
t½ = ln 2 = 0.693
k
k
3
Half Life
Half Life
t1/2(239Pu) = 24,400 years:
Decay Process
238
234
+
92U →
90 Th
H→
3
2
C→
14
7
I →
131
54
3
1
14
6
131
53
123
53
I+
4
2
He
Half-life
4.15 x 109 y
He +
0
-1
e
12.3 yr
N
+
0
-1
e
5730 yr
Xe +
0
-1
e
8.04 d
e →
0
-1
123
52
Te
13.2 h
Cr →
57
25
e
21 s
28
15
P→
28
14
Si
+
0
+1
e
0.270 s
90
38
Sr →
90
39
Y
+
0
-1
e
28.8 yr
60
27
Co →
60
28
Ni
+
0
-1
e
5.26 yr
57
24
Mn +
0
-1
Half-Life
Rate of Radioactive Decay
192Ir
The activity (A) of a sample of N atoms:
A = (disintegrations/time) observed.
A = (constant) N
constant = k if all decays are detected…
decays with a rate constant of 9.3 x 10-3 d-1
(a) What is t1/2 for 192Ir ? (b) What fraction of a 192Ir
sample would remain after 100 days?
(a) t1/2 = (ln 2)/ k = (0.693)/(9.3 x 10-3 d-1) = 74.5 d
(b)
ln
N
= -kt = -(9.3 x 10-3 d-1)(100 d) = -0.930
N0
At t = 0 the activity
At a later time, t
N
= e-0.930 = 0.394
N0
Then:
A0 = (constant) N0
A = (constant) N
A = N = fraction of atoms remaining
A0 N0
39% of the original sample remains.
Rate of Radioactive Decay
Rate of Radioactive Decay
Geiger counter: an Ar-filled tube under high voltage.
Since:
ln Nt = −kt + ln N0
or
ln N = -kt
N0
ln A = -kt
A0
As usual
t½ =
ln 2 0.693
=
k
k
1 becquerel (Bq) = 1 disintegration/sec (s-1).
1 curie (Ci) = 3.7 x 1010 s-1 = decay rate of 1g of Ra.
4
Carbon-14 Dating
Carbon-14 Dating
n0
High-energy cosmic rays eject from atoms in the
upper atmosphere. 14C is produced by collision:
14
7
N +
1
0n
14
6C
+
1
1H
• World-wide production of 14C ≈7.5 kg/year. It is:
• Evenly distributed
• Converted into 14CO2, then sugars (photosynthesis).
Mammals eat the plants…
Activity (living organisms) = 15.3 min-1 g-1 of carbon.
After death the uptake stops. Stored 14C decays.
t½ (14C ) = 5.73 x 103 years.
Used to measure up to ≈ 9 half-lives ( ≈ 50,000 years)
A0 = 15.3 min-1 g-1
A50,000y = 0.030 min-1 g-1
≈ 2 h-1 g-1
Longer times are difficult to
measure reliably.
Prehistoric cave painting
Nuclear Fission
Nuclear Fission
Hahn and Strassman (1938) fired n0 at 135U. Ba was
produced!
Chain reactions are possible:
Small amounts of 235U
can’t capture all n0.
Nuclear fission had occurred.
235
92 U
1
+ 0n
236
92 U
141
56 Ba
92
1
+ 36 Kr + 3 0 n
3 n0
produced
Very
exothermic
Nuclear Reactors
Efission(235U) = 2 x 1013 J/mol.
1 kg of 235U ≈ 33 kilotons of TNT.
Natural U is 99.3%
238U (not fissile).
Reactor fuel rods are
enriched to 3% 235U.
Weapons-grade is
> 90% 235U.
(stays under control).
Nuclear bombs exceed
the critical mass; the
chain reaction grows
explosively.
Nuclear Reactors
Nuclear power-plants produce “clean” energy.
• No atmospheric pollution. No CO2.
But… yield highly radioactive waste
• Tens of thousands of tons in storage
• Long half-lives (239Pu, t1/2 = 24,400 yr)
• Can be vitrified (encased in “glass”)
• Vwaste = 2 m3/reactor/yr.
• Yucca Mountain, NV (salt dome).
104 nuclear plants in the U.S. None built
since 1979 (Three Mile Island).
5
Nuclear Fusion
Light atoms can be joined:
1
4 1H
Nuclear Fusion
Unfortunately, fusion is hard to produce on earth:
4
2 He
+ 2
0
+1e
Nuclear fusion.
• Very exothermic (ΔE = -2.5 x 109 kJ/mol ).
• The energy source for stars.
• H-atoms must be converted into a plasma – a soup
of bare nuclei and e-.
• T > 108 K required.
• The plasma is hard to contain,
 magnetic “bottles” are used.
An attractive power source:
• Hydrogen (the fuel) can be
extracted from oceans.
• Waste products are short-lived,
low-mass isotopes.
Commercial fusion reactors are not very likely to occur
in the near future.
Fusion powers the sun
Nuclear Radiation: Effects & Units
Nuclear Radiation: Effects & Units
rad
, , and  have different biological effects, so…
radiation absorbed dose.
1 rad = 0.010 J absorbed/kg of material
gray (Gy)
SI unit.
rem
roentgen equivalent in man.
dose in rem = (quality factor) x (dose in rads)
1 Gy = 1 J absorbed/kg of material
1 Gy = 100 rad
Roentgen (R) dosage of X-ray and -radiation.
R = 9.33 µJ deposited/g of tissue
Background Radiation
sievert (Sv) SI version. 1 Sv = 100 rem
Quality factors:  = 10 - 20,  = 1,  = 1
Radon
Produced by naturally occurring U-deposits in the soil.
An inhalation hazard:
218
84Po
222
Rn
86
+
4
He
2
Po(s) remains in the lungs and decays:
218
Po
84
214
Pb
82
+
4
He
2
A common household hazard.
Key: Source % of total (millirems/yr)
6