1 mole of radioactive substance X disintegrates by $$\alpha$$-emission. Its half life time is 10 days. After 20 days the amount of Helium gas liberated at STP (in litres) is _____________

Correct Answer: 16.8

Solution

20 days is two half-lives, so $$\frac{1}{4}$$ mol of X remains and $$\frac{3}{4}$$ mol has decayed. Each decay emits one $$\alpha$$ particle, which becomes one He atom, giving 0.75 mol of helium. At STP this occupies $$0.75 \times 22.4 = 16.8\text{ L}$$.

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