Question

Two radioactive isotopes P and Q have half-lives of 10 minutes and 15 minutes, respectively. Freshly prepared samples of each isotope initially contain the same number of atoms as one another, After 30 minutes, the ratio of $\frac{thenumberofatomsofP}{thenumberofatomsofQ}$ will be then:

• A. 0.6
• B. 0.5
• C. 0.8
• D. 0.9

Answer 1

The correct option is B 0.5

assuming both $P$ & $Q$ atom are initially present $N_0$ in number.

Given,

Half-line of $P\left(z_1\right)=10minute$

Half-line of $Q\left(z_2\right)=15minute$

From rate law expression, at time $t$,

$N_t=N_0{\left(\frac{1}{2}\right)}^{t/z}$

so, putting values,

$\frac{N_{t1}}{Nt2}=\frac{{\frac{1}{2}}^{30/10}}{{\frac{1}{2}}^{30/15}}\Rightarrow$ $\frac{N_{t1}}{N_{t2}}=\frac{1}{2}$