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Question: A sample contains large number of nuclei. The probability that a nucleus in sample will decay after ...

A sample contains large number of nuclei. The probability that a nucleus in sample will decay after four half lives is-

A

14\frac{1}{4}

B

34\frac{3}{4}

C

1516\frac{15}{16}

D

716\frac{7}{16}

Answer

1516\frac{15}{16}

Explanation

Solution

Probability that a nucleus will not decay is-

(NN0)\left( \frac { \mathrm { N } } { \mathrm { N } _ { 0 } } \right) = (12)n\left( \frac { 1 } { 2 } \right) ^ { \mathrm { n } } = q When n is the no. of half lives q = (12)4\left( \frac { 1 } { 2 } \right) ^ { 4 }

= 116\frac { 1 } { 16 } Probability that a nucleus will decay is

p = 1 – q = 1 –116\frac { 1 } { 16 }= 1516\frac { 15 } { 16 }