Question

At any instant the ratio of the amount of radioactive substance is 2 : 1. If their half lives be respectively 12 and 16 hours, then after two days, the ratio of the substances is

• A. 1:01
• B. 2:01
• C. 1:02
• D. 1:04

Answer 1

Answer: (A)

1:01

Answer 2

For first substance $n = \frac{48}{12} = 4$ Hence $N_1 = N_{01} \left( \frac{1}{2} \right)^4 = \frac{N_{01}}{16}$ For second substance $n = \frac{48}{16} = 3$ Hence $N_2 = N_{02} \left( \frac{1}{2} \right)^3 = \frac{N_{02}}{8}$ $\Rightarrow$ $\frac{N_1}{N_2} = \frac{N_{01}}{N_{02}} \times \frac{1}{2}$ But $N_{01} = 2 \, \, n_{02}$, hence $\frac{N_1}{N_2} = 1$