Answer to Question #261337 in Atomic and Nuclear Physics for Ytz

Question

How long will it take for a 10-mCi (370 MBq) sample of 32P(t1/2 ¼ 14.3 days) and a 100-mCi(3.7 GBq)sampleof67Ga(t1/2 ¼ 3.2 days) topossess the same activity?

Answer 1

$A_1=A_{01}2^{-\frac t{T_{1/2,~1}}},$

$A_2=A_{02}2^{-\frac t{T_{1/2,~2}}},$

$A_1=A_2,\implies$

$t=\frac{T_1T_2}{T_1-T_2}\log _2 \frac{A_{02}}{A_{01}}=13.7^h.$