Question

10 g atoms of an $\alpha$-active radioactive isotope are disintegrating in a sealed container. In one hour, the $He$ gas collected at STP is 11.2 cm${}^3$. Calculate half-life of radioactive isotope?

• A. 1.582 years
• B. 1.782 years
• C. 1.682 years
• D. None of these

Answer 1

The correct option is A 1.582 years

Initial amount of an $\alpha$-active isotope $=N_0=10g$ atom
Helium formed = 11.2 cc at STP
$=\frac{11.2}{22400}g$ atom at STP
$=5\times {10}^{-4}$ g atom
$\therefore$ Element left $=(10-5\times {10}^{-4}$
= 9.9995 g atom
$\lambda =\frac{2.303}{t}log\frac{N_o}{N}$
$=2.303log\frac{10}{9.9995}=5\times {10}^{-5}{h}^{-1}$
$t_{50}=\frac{0.693}{\lambda }=\frac{0.693}{5\times {10}^{-3}h}$
=13857 h = 1.582 years