The radioactive decay rate of a radioactive element is found to be 10³disintegrations/sec., at a certain time. If half-life of the element is one second, what would be the decay rate after 1 sec., and after 3 sec.?

Solution

Radioactive decay rate is directly proportional to the number of nuclei left.

N_{0}

= 10³disintegrations/sec.

Half-life, T = 1 sec.,

Therefore,

(i) Number of half lives in 1 sec., n = 1

As,

N = N_{0} {(\frac{1}{2})}^{n}

∴

N = 1000 {(\frac{1}{2})}^{1} = 500

∴

Number of disintegrations/sec. after one sec. = 500
(ii) Number of half lives in 3 sec. = n =

\frac{3}{1} = 3

As,

N = N_{0} {(\frac{1}{2})}^{n}

∴

N = 1000 {(\frac{1}{2})}^{3} = \frac{1000}{8} = 125

Therefore, number of disintegrations per second after three second is 125.

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