Two samples A and B contain equal amount of radioactive substances. If (1/8)th of sample A and (1/128)th of sample B, remain after 9 hours, then the ratio of half life period of B to that of A is (a) 9: 7 (b) 7: 3 (c) 3: 7 (d) 3: 1

Answer: (c). A: 1/8 = (1/2)³, so 3 half-lives in 9 h, TA = 3 h. B: 1/128 = (1/2)⁷, so 7 half-lives in 9 h, TB = 9/7 h. TB: TA = 9/7: 3 = 3: 7. So the answer is (c) 3: 7.

Two samples A and B contain equal amount of radioactive substances… | MHT CET 2026 (18 Apr, Shift 2)

Q11MHT CET 2026 · 18 APR · SHIFT 2Medium

Law of Radioactive Decay

Two samples A and B contain equal amount of radioactive substances. If $\left(\frac{1}{8}\right)^{th}$ of sample A and $\left(\frac{1}{128}\right)^{th}$ of sample B, remain after 9 hours, then the ratio of half life period of B to that of A is

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Answer: (c)

A: $1/8 = (1/2)^3$ , so 3 half-lives in 9 h, $T_A = 3$ h.
B: $1/128 = (1/2)^7$ , so 7 half-lives in 9 h, $T_B = 9/7$ h.
$T_B : T_A = \frac{9}{7} : 3 = 3 : 7$ .
So the answer is (c) $3 : 7$ .

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