Question

The activity of a radioactive sample is A₁ at time t₁ and A₂ at time t₂. If t is average life of sample then the number of nuclei decayed in time (t₂ – t₁) is-

• A. A₁ t₁ – A₂ t₂
• B. $\frac{(A_{1} - A_{2})}{2}\tau$
• C. (A₁ – A₂) (t₂ – t₁)
• D. (A₁ – A₂) t

Answer 1

Answer: (D)

(A₁ – A₂) t

Answer 2

Let N₀ be the initial number of nuclei, then

N₁= and

\ number of nuclei decayed = N₁ – N₂

= = $\frac { \mathrm { A } _ { 0 } } { \lambda } \left( \mathrm { e } ^ { - \lambda _ { 1 } \mathrm { t } } - \mathrm { e } ^ { - \lambda _ { 2 } \mathrm { t } } \right)$

= $\frac { \mathrm { A } _ { 1 } - \mathrm { A } _ { 2 } } { \lambda }$ = (A₁ – A₂)t