JEE Main 2022 · 24 Jun · Shift 2 · Physics Q56

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PhysicsInteger+4 / -1Question 56 of 90

A sample contains $10^{-2}$ kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is $\dfrac x{100}$ . The value of $x$ is ______.

Your answer

Answer and worked solution

Official answer: 25

Half-lives elapsed in 16 s. A: $16/4=4$ , so $\frac1{16}$ of A remains. B: $16/8=2$ , so $\frac14$ of B remains.

Amounts (masses), starting equal. $\dfrac{m_A}{m_B}=\dfrac{1/16}{1/4}=\dfrac14=\dfrac{25}{100}$ , so $x=25$ (the keyed value).

Note. Counting moles instead, the 1 : 2 atomic weights double A's share and give $\frac12$ ; the key takes "amount" as mass.

Answer: 25

Topics:Radioactive decay

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JEE Main 2022 · 24 Jun · Shift 2, Physics question 56