Half Life
factors will affect the rate
of a chemical reaction?
 What
Half Life
 Temperature
 Pressure
 Concentration
Half Life
factors will affect the rate
of a nuclear reaction?
 Nuclear reactions are NOT
dependent on temperature,
pressure, or concentration!
 What
 Their
rates are constant!
of reactants
Half Life
 Radioactive
decay is a random
event, determined by probability
 We don’t know which atoms will
decay in a certain amount of time
 We do know how many will
decay, on average, in a certain
amount of time
Half Life
 Half
life
 the
time it takes for exactly half of
the atoms in a sample to undergo
nuclear decay
radioisotope has a unique
half life
 Each
1
Half Life
shorter the half life, the more
unstable the isotope is
 Table N in the Reference Tables
lists selected isotopes, their
half lives, and their mode of
radioactive decay
 The
Problem
 Cr-51
is an unstable isotope with
a half life of 28 days
 What fraction of a Cr-51 sample
will remain after 168 days?
 If a Cr-51 sample has an original
mass of 52.0 g, what mass will
remain after 168 days?
#H-L
Time (d) Mass (g) Frac R
0
0
52
100
1
28
26
0.50
2
56
13
0.25
3
84
6.5
0.125
4
112
3.25
0.0625
5
140
1.625
0.03125
6
168
0.8125
0.015625
Half Life
 For
more complex problems, we
will use the radioactive decay
formula, which is NOT in the
reference tables
 N = (N0)(1/2)t/T
2
Half Life
 Fraction
remaining = N/N0 = (1/2)t/T
= size of original sample
 N = size of remaining sample
after time t
 t = elapsed time
 T = half life of isotope
 t/T = number of elapsed half-life
periods
 N0
Problem
many half lives are required
for a radioisotope to decay to 1/32
of its initial mass?
 How
Solution
= (1/2)t/T
 log[1/32] = log[(1/2)t/T]
 log[1/32] = (t/T)(log[1/2])
 t/T = (log[1/32])/(log[1/2])
 # half-life periods = t/T = 5
 1/32
Solution
 According to Table N, the halflife of 16N is 7.13 seconds
 t = 28.52 s; T = 7.13 s
 Frac R = (1/2)28.52/7.13 = 0.0625
 massf = (massi)(Frac R)
 massf = (100 )(0.0625)
 massf = 6.25 μg will remain
Problem
 How much of a
16N will remain
100 μg sample of
after 28.52 s of
decay?
Problem
 The
half life of a radioisotope is
3.1 hours
 How much of a 10.0 g sample
will remain unchanged after 9.3
hours?
3
Solution
Problem
# H-L
Time (h) Mass (g) Frac R
0
0
10
1.0
1
3.1
5
0.5
2
6.2
2.5
0.25
3
9.3
1.25
0.125
 After
a period of 1000 years, only
62.5 g of an original 1 kg sample
of a radioisotope remains
unchanged
 What is the half life of the
radioisotope?
Solution
# H-L
0
Time (y) Mass
(kg)
0
1
Solution
Frac R
1.0
1
0.5
0.5
2
0.25
0.25
3
0.125
0.125
0.0625
0.0625
4
1000
x
+ x + x + x = 1000 y
 4x = 1000 y
 x = (1000 y)/4 = 250 y
Solution
= (1/2)t/T
 T = t/(#H-L) = (1000 y)/4 = 250 y
 #H-L
Solution
# H-L
Fraction
0
Time (y) Mass
(kg)
0
1
1
250
0.5
0.5
2
500
0.25
0.25
3
750
0.125
0.125
4
1000
0.0625
0.0625
1.0
4