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Q.

$_{87}^{221} Ra$ undergoes radioactive decay with a half life of 4 days. The probability that a Ra nucleus will disintegrate in 8 days is

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a

1

b

1/2

c

1/4

d

3/4

answer is D.

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Detailed Solution

$n = \frac{t}{t_{1 / 2}} = \frac{8}{4} = 2; N_{o} = 2^{n} N; \frac{N_{o}}{N} = 2^{2} = 4$
$Remaining atoms = N = \frac{N_{o}}{4}$
$\begin{array}{l} Dacayed atoms = N_{0} - N = N_{0} - \frac{N_{0}}{4} = \frac{3 N_{0}}{4} \\ ∴ Probability of decay = \frac{N_{0} - N}{N_{0}} = \frac{3}{4} \end{array}$

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