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Question: A radioactive material of half-life T was produced in a nuclear reactor at different instants, the q...

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

Tln2ln2A1A2\frac{T}{\ln 2}\left| \ln\frac{2A_{1}}{A_{2}} \right|

B

TlnA1A2\left| \ln\frac{A_{1}}{A_{2}} \right|

C

Tln2lnA22A1\frac{T}{\ln 2}\left| \ln\frac{A_{2}}{2A_{1}} \right|

D

TlnA22A1\left| \ln\frac{A_{2}}{2A_{1}} \right|

Answer

Tln2lnA22A1\frac{T}{\ln 2}\left| \ln\frac{A_{2}}{2A_{1}} \right|

Explanation

Solution

A1 =

Ž t1 = 1λ\frac { 1 } { \lambda }ln (λN0 A1)\left( \frac { \lambda \mathrm { N } _ { 0 } } { \mathrm {~A} _ { 1 } } \right)

A2 = l(2N0) eλt2\mathrm { e } ^ { - \lambda \mathrm { t } _ { 2 } }

Ž t2 = 1λ\frac { 1 } { \lambda }ln (2λ N0 A2)\left( \frac { 2 \lambda \mathrm {~N} _ { 0 } } { \mathrm {~A} _ { 2 } } \right)

so t1 – t2 = 1λ\frac { 1 } { \lambda } ln(A22 A1)\left( \frac { \mathrm { A } _ { 2 } } { 2 \mathrm {~A} _ { 1 } } \right)=ln(A22 A1)\left( \frac { \mathrm { A } _ { 2 } } { 2 \mathrm {~A} _ { 1 } } \right)