Question

Two elements $P$ and $Q$ have half-lives of 10 and 15 minute respectively. A freshly prepared sample of a mixture containing the equal number of atoms is allowed to decay for 30 minutes.

The ratio of the number of atoms of $P$ and $Q$ left in the mixture is:

• A. 0.5
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (A)

0.5

In 30 minute,

P completes 3 half time, so its remaining atoms, $N_P=N_0/2^3$

Q completes 2 half time and its remaining atoms, $N_Q=N_0/2^2$

$N_P=N_{0_P}{e}^{-\frac{0.693}{10}\times 30}=N_0{e}^{-0.693\times 3}$

$N_Q=N_{0_Q}{e}^{-\frac{0.693}{15}\times 30}=N_0{e}^{-0.693\times 2}$

$\therefore \frac{N_P}{N_Q}=e^{-0.693}=0.5$