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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-

= = q When n is the number 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 }