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JEE Advanced levelSingle correct optionDifficulty 3 of 3as186

A sample of $N_{0}$ atoms has a half-life of $10$ min. The number of atoms that decay between $t = 15$ min and $t = 30$ min is closest to

A $0.354 N_{0}$
B $0.125 N_{0}$
C $0.500 N_{0}$
D $0.229 N_{0}$

Answer: D

Atoms left at 15 min

= N_{0} 2^{- 1.5} = 0.354 N_{0}

; at 30 min

= N_{0} 2^{- 3} = 0.125 N_{0}

. Number decaying in the interval

= 0.354 N_{0} - 0.125 N_{0} = 0.229 N_{0}

.

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