Question

1 g atom of an $\alpha$ - emitting ${}_z{X}^A$ (half life = 10 hr) was placed in sealed containers. $4.52\times {10}^{23}$ helium atoms will accumulate in the container after :

• A. 4.52 hr
• B. 10.00 hr
• C. 9.40 hr
• D. 20.00 hr

Answer 1

The correct option is D 20.00 hr

The radioactive decay follows first order kinetics.
Rate constant k = $\frac{0.693}{t_{1/2}}$
Given, $t_{1/2}=10hour$
$k=0.0693$
Also, k = $\frac{2.303}{t}\times log\frac{N_o}{N_t}$
$N_o=1.0$ (1 g atom = 1 mole)
No.of moles of He = $\frac{4.52\times {10}^{23}}{6.023\times {10}^{23}}$
= 0.75
$N_t=1-0.75=0.25$
Substituting the values we get, t = 20.0 hour.