Question

The decay constant of a radioactive isotope is $\lambda$ if $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively then the number of nuclei which have decayed during the time $\left( t_{1} - t_{2} \right)$

• A. $A_{1}t_{1} - A_{2}t_{2}$
• B. $A_{1} - A_{2}$
• C. $\left( A_{1} - A_{2} \right)/\lambda$
• D. $\lambda\left( A_{1} - A_{2} \right)$

Answer 1

Answer: (C)

$\left( A_{1} - A_{2} \right)/\lambda$

Answer 2

: $A_{1} = \lambda N_{1}$at time $t_{1}$

$A_{2} = \lambda N_{2}$at time $t_{2}$

Therefore, number of nuclei decayed during time interval $(t_{1} - t_{2})$ is

$N_{1} - N_{2} = \frac{(A_{1} - A_{2})}{\lambda}$