Half Life class 10 | 10th class physics ch 18 half life and its measurement | physics wallah sabaq

Half Life class 10 | 10th class physics ch 18 half life and its measurement | physics wallah sabaq
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18.5 HALF-LIFE AND ITS MEASUREMENT
Process of radioactivity is random and the rate of
radioactive decay is proportional to the number of unstable
nuclei present. In the process, a constant fraction of large
number of unstable radioactive nuclei decays in a certain
time. So the life time of the unstable nuclei is unlimited and
is difficult to measure. We can get the idea about decay
rate by the term half-life.
Half-Life
The time during which half of the unstable radioactive
nuclei disintegrate is called the half-life of the sample of
radioactive element.
Every radioactive element has its own characteristic half life. For example, radium-226 has a half-life of 1620 years,
which means that half of a radium-226 sample will be
converted to other elements by the end of 1620 years
(Fig.18.7). In the next 1620 years, half of the remaining
radium will decay, leaving only one-fourth the original
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,
Remaining atoms = Original atoms
t
1/2
or N = N x 1/
t
o 2
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.
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 is the half-life and
T
A is the original
½
o
activity of the sample. After time T activity will be /2.
½
Ao
After 2T activity will become1/2. /2= /4. While after
½
A A
o o
time 3T , i.e., after three half-lives, the activity will drop
½
to /8. It means activity drops to one-eighth of original
Ao
activity in a time of 3 .T
½
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
radioactive decay of the element.
Solution: The initial count rate is 1000, therefore,
(a) As clear from above, it takes 2 half-lives for the count rate
181
ATOMIC AND NUCLEAR PHYSICS
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