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Q.

At a given instant there are 25% of undecayed radio– active nuclei in a sample. After 10S, the number of undecayed nuclei reduces to 12.5%. The time in which the number of undecayed nuclei will further reduced to 6.25% of the reduced number is,

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a

20 Sec

b

30 Sec

c

10 Sec

d

40 Sec

answer is C.

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Detailed Solution

$\begin{aligned} N = N_{0} {(\frac{1}{2})}^{n} \\ 6.25 = 100 {(\frac{1}{2})}^{n} \\ 2^{n} = 16 \\ n = 4 \\ S o t i m e t a k e n (t o t a l) = 40 s \\ H e n c e f u r t h e r t i m e t a k e n t o r e d u c e f r o m 12.5 % t o 6.25 % = 40 - 30 = 10 s \end{aligned}$

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