Question

A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are A₁ and A₂ respectively then their age difference equals-

• A. $\frac{T}{\ln 2}\left| \ln\frac{2A_{1}}{A_{2}} \right|$
• B. T$\left| \ln\frac{A_{1}}{A_{2}} \right|$
• C. $\frac{T}{\ln 2}\left| \ln\frac{A_{2}}{2A_{1}} \right|$
• D. T$\left| \ln\frac{A_{2}}{2A_{1}} \right|$

Answer 1

Answer: (C)

$\frac{T}{\ln 2}\left| \ln\frac{A_{2}}{2A_{1}} \right|$

Answer 2

A₁ =

Ž t₁ = $\frac { 1 } { \lambda }$ln $\left( \frac { \lambda \mathrm { N } _ { 0 } } { \mathrm {~A} _ { 1 } } \right)$

A₂ = l(2N₀) $\mathrm { e } ^ { - \lambda \mathrm { t } _ { 2 } }$

Ž t₂ = $\frac { 1 } { \lambda }$ln $\left( \frac { 2 \lambda \mathrm {~N} _ { 0 } } { \mathrm {~A} _ { 2 } } \right)$

so t₁ – t₂ = $\frac { 1 } { \lambda }$ ln$\left( \frac { \mathrm { A } _ { 2 } } { 2 \mathrm {~A} _ { 1 } } \right)$=ln$\left( \frac { \mathrm { A } _ { 2 } } { 2 \mathrm {~A} _ { 1 } } \right)$