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JEE Main levelOne or more correct optionsDifficulty 2 of 3as182

A radioisotope with half-life $10$ min undergoes first-order decay. Take $ln 2 = 0.693$ . Which statements are correct?

A $12.5%$ of the initial atoms remain after $30$ min.
BThe decay constant is $0.0693 mi n^{- 1}$ .
C $50%$ of the initial atoms have decayed after $20$ min.
DThe activity falls to one half every $10$ min.

Answer: A, B, D

After 30 min, 3 half-lives:

(1/2)^{3} = 12.5%

remain (A true).

λ = 0.693/10 = 0.0693 mi n^{- 1}

(B true). After 20 min, 25% remain so 75% decayed, not 50% (C false). Activity is proportional to

N

, so it halves every half-life (D true).

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