Q. Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to :

Solution:

at t = 0, $A_0 = \frac{dN}{dt} = 1600 C/s$
at t = 8s, A = 100 C/s
$\frac{A}{A_0} = \frac{1}{16} $ in 8 sec
Therefor half life is $t_{1/2} = 2 \; \sec$
$\therefore$ Activity at t = 6 will be $1600 ( \frac{1}{2} )^3$
= 200 C/s
$\therefore$ correct answer is (3)

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