Two radioactive sample A and B have half $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. At $T = 0$ , the activity of a B was twice the activity of A. Their activity will become equal after a time :
$\frac{T_{1} T_{2}}{T_{1} - T_{2}}$
$\frac{T_{1} - T_{2}}{2}$
$\frac{T_{1} + T_{2}}{2}$
$\frac{T_{1} T_{2}}{12}$

Question

Two radioactive sample A and B have half $T_{1}$ and $T_{2}$ $(T_{1} > T_{2})$ respectively. At $T = 0$ , the activity of a B was twice the activity of A. Their activity will become equal after a time :
$\frac{T_{1} T_{2}}{T_{1} - T_{2}}$
$\frac{T_{1} - T_{2}}{2}$
$\frac{T_{1} + T_{2}}{2}$
$\frac{T_{1} T_{2}}{12}$

Toppr Admin · Accepted Answer

Consider initial activity of nuclei A and B be A0 and 2A0 respectively-xA0- at a time -x2032-t-x2032- their activity is given by-A1A0e-x2212-x3BB-t -for A - A2-2A0e-x2212-x3BB-t -for B-where -x3BB-ln2T -T-half -life-When A1-A2 at time -apos-t-apos-A0e-x2212-ln2T1t-2A0e-x2212-ln2T2t -x3BB-1-m2T1 and -x3BB-2-ln2T2-Take log of both sides -x2212-m2T1t-x2212-m2T2-ln2-x2212-tT1-x2212-tT2-1-t-T1T2T1-x2212-T2

Two radioactive sample A and B have half T1 and T2(T1>T2) respectively. At T=0, the activity of a B was twice the activity of A. Their activity will become equal after a time :T1T2T1−T2T1−T22T1+T22T1T212