Question

The half life period of uranium is $4.5$ billion years. After $9.0$ billion years, the number of moles of helium liberated from the following nuclear reaction will be:
${}_{92}^{238}U⟶$ ${}_{90}^{234}Th{+}_2^{4}He$
Initially there was $1$ mole uranium.

• A. $0.75mol$
• B. $1.0mol$
• C. $11.2mol$
• D. $22.4mol$

Answer 1

The correct option is A $0.75mol$

${}_{92}^{238}U⟶{}_{90}^{234}Th{+}_2^{4}He$

$\Rightarrow$1 mole of ${}_{92}^{238}U$ will form 1 mol of He[mole concept]

Amount of Uranium remaining after 9 billion years.

$=\frac{1}{{\left(2\right)}^2}\times \left(1mole\right)$

= 0.25 mole

Amount used = 0.75 mole

$\therefore$Moles of Helium formed = 0.75 mole. in 9 billion years.