Question

The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old ${}^{32}P(t_{\frac{1}{2}}=14.3\text{days})$ source if it was originally purchased for 800 rupees ?

Answer 1

Given $t_{\frac{1}{2}}=14.3\text{days}$

$t=30\text{days}=1\text{month}$

As the selling rate is decided by the activity,

hence $A_0=800$ disintegration/sec.

We know $A=A_0{e}^{-\lambda t}$

i.e. $A=800\times e^{\frac{-0.698}{14.3}}\times 30$

=$800\times 0.233669$

$=186.935=187$