Page 181 - Physics 10_Float

ATOMIC AND NUCLEAR PHYSICS

If the half-life of the radioactive element is T , then at the
1/2
end of this time the number of atoms in the sample will
become half i.e., 1/2. After a time 2T , i.e., after second half-
1/2
life period, the number of remaining atoms will become
2
1/2.1/2 =1/2 =1/4, after a time 3 T , the number of
1/2
3
remaining atoms left will be1/2.1/2.1/2 =1/2 =1/8 , and at
the end of ‘t’ half lives number of atoms that remain will be
t
1/2 . It means that if N is the original number of atoms in the
o
sample of radioactive element, then after ‘t’ half-lives
number of atoms left in the sample can be determined by
using the relation,
t
Remaining atoms = Original atoms 1/2
t
or N = N x 1/2
o
The process of radioactivity does not depend upon the
.
chemical combinations or reactions. It is also not affected by
any change in physical conditions like temperature, pressure,
electric or magnetic fields. Be careful !

Example 18.2: The activity of a sample of a radioactive
bismuth decreases to one-eight of its original activity in
15 days. Calculate the half-life of the sample.

Solution: Let T ½ is the half-life and A is the original
o
activity of the sample. After time T activity will be /2.
A
½
o
After 2T activity will become1/2. /2= /4. While after
A
A
½ o o
time 3T , i.e., after three half-lives, the activity will drop International symbol that
½ indicates an area where
to /8. It means activity drops to one-eighth of original A
o radioactive material is being
activity in a time of 3 .T ½ handled or produced.
Therefore, 3T = 15. This means half-life T of the sample will
½
½
be 5 days.
Example 18.3: A radioactive element has a half-life of
40 minutes. The initial count rate was 1000 per minute. How
long will it take for the count rate to drop to (a) 250 per
minutes (b) 125 per minutes (c) Plot a graph of the Radiation Treatment
radioactive decay of the element. Gamma radiations destroy
Solution: The initial count rate is 1000, therefore, both cancerous cells and
40 min.
40 min.
40 min.
1000 500 250 125 healthy cells. Therefore, the
beam of radiation must be
directed only at cancerous
(a) As clear from above, it takes 2 half-lives for the count rate cells.
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