Question

Two radioactive nuclides A and B have half lives of 50 min and 10 min respectively. A fresh sample contains the nuclides of B to be eight time that of A. How much time should elapse so that the number of nuclides of A becomes double of B?

• A. 30
• B. 40
• C. 50
• D. None

Answer 1

The correct option is C 50

$N_{0B}=8N_{0A}$
After one half life period of A (50 min), $N_A=\frac{N_{0A}}{2}$......(1)
During the same time (which is equal to 5 half life periods of B), $N_B=\frac{N_{0B}}{2^5}=\frac{N_{0A}}{4}$......(2)
From equations (1) and (2),
$N_A=2N_B$