Question

A rate-meter measures the number of disintegrations per second from a radioactive source. It gives a count of $320$ counts per second. Ninety minutes later, it gives $40$ counts per second. The half life of the source is

• A. $30mnts$
• B. $45mnts$
• C. $60mnts$
• D. $75mnts$

Answer 1

The correct option is A $30mnts$

We know that the formula for disintegration after n half lives

$\frac{N}{N_o}={\left(\frac{1}{2}\right)}^n$

According to question it is given that $N_o=320countspersecond$ and

$N=40countspersecond$

Hence, $\frac{40}{320}={\left(\frac{1}{2}\right)}^n$

$⟹\frac{1}{8}={\left(\frac{1}{2}\right)}^n$

$⟹n=3$

And , time $t=n\times t_{\frac{1}{2}}$ where $t_{\frac{1}{2}}$ is the half life of the radio-active substance.

$⟹t_{\frac{1}{2}}=\frac{t}{n}$ and $t=90min$

Hence, half-life $t_{\frac{1}{2}}=30min$

Answer is -(A)