Question

A radioisotope isotope ${}_Z^m\text{A}(t_{1/2}=10day)$ decays to give ${}_{Z-6}^{m-12}\text{B}$ stable atom along with $\alpha$-particles. If $m$ g of $A$ are taken and kept in a sealed sealed tube, volume of He in litre will accumulate in 20 day at STP is_________.

(If the answer is X, then write 10X).

Answer 1

The nuclear reaction is
${}_Z^m\text{A}⟶{}_{Z-6}^{m-12}\text{B}+3{}_2^4\text{He}$
Given, the half life period $t_{1/2}=10day$; time for decay $t=20day$; Initial amount of decay $N_0=mg=1g-atom$
The number of half life periods present in the decay time $=n=\frac{T}{t_{1/2}}=\frac{20day}{10day}=2$
Amount left in 2 half lives $=(1/2{)}^2=\frac{1}{4}g-atom$
Amount of A decayed in 2 half lives $=(1-\frac{1}{4})=\frac{3}{4}g-atom$
$\because$ 1 g-atom of $A$ gives 3 mole of He at STP
$\therefore \frac{3}{4}$ g atom of A will give $3\times \frac{3}{4}$ mole of He at STP$=\frac{9}{4}$ mole of He at STP Volume of He at STP$=\frac{9}{4}\times 22.4litre=50.4$ litre at STP.