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JEE Advanced levelSingle correct optionDifficulty 3 of 3as185

Nuclides A and B have half-lives of $2 h$ and $6 h$ respectively, and their activities are equal at $t = 0$ . At what time is the activity of B twice that of A?

A3 h
B6 h
C1.5 h
D4 h

Answer: A

A_{B} / A_{A} = 2^{- t /6} / 2^{- t /2} = 2^{t /2 - t /6} = 2^{t /3}

. Setting this equal to 2 gives

t /3 = 1

, so

t = 3 h

.

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