Question

Radiation emitted from a radioactive element, of half life period of $30$ min, are measured by a Geigar - Mullar counter. The count rate of the sample reduces to $5$ disintegrations /sec. in $2hrs$. then the initial count rate in disintegration/sec is :-

• A. $805$
• B. $200$
• C. $250$
• D. $40$

Answer 1

The correct option is A $805$

[A]

Half life = 30 mins

N = 5 / sec

Time = 120 min

$\begin{array}{c}\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{Time}{halflife}}={\left(\frac{1}{2}\right)}^{\frac{120}{30}}=\frac{1}{16}\\ N_0=16\times N={805}^{-1}\end{array}$