Radioactivity and
radioisotopes
• Decay Constant and Half-life
• Exponential law of decay
Decay constant and half-life
It is possible to relate the decay constant  to
the half-life T½.
We already said that N0 is the number of
radioactive atoms for t = 0.
So, ½N0 will be the number of radioactive atoms
after one half-life t = T½.
1
 T1 / 2
N 0  N 0e
2
1
 T1 / 2
e
2
Decay constant and half-life
Using logarithms to base e, solve the last
equation to find the relationship between 
and T½.
Half-life
We measure the activity of a radioactive isotope in
BEQUERELS (Bq), i.e. no of disintegrations per sec.
Use the table to draw the half-life graph of Iodine-128.
Time
(min)
Activity
(Bq)
0
40
25
20
50
10
75
5
Exponential law of decay
Using a similar reasoning to the discussion on
half-life and number of undecayed atoms N,
we can conclude that:
Where A is the activity (in Bq) at time t, A0 is the
activity for t = 0 and x the number of half-lives
elapsed.
Activity and number of
radioactive atoms
A very useful equation is the relationship
between the activity of a radioactive nuclide
and the number of radioactive atoms:
Questions
1.
Polonium 210 has a half-life of approximately 138 days. At
the beginning of an investigation the sample contains 2 g of
Po-210. How long will it take to have 1/32 g of Po-210?
2.
Plot the graph of N = N0e-t for values of t between 0 – 10 s.
What is the half-life if N0 = 6.2 x 1012 and  = 0.25 s-1?