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Question: Half-life of a radioactive substance A is two times the half-life of another radioactive substance B...

Half-life of a radioactive substance A is two times the half-life of another radioactive substance B. Initially the number of nuclei of A and B are NA and NB respectively. After three half lives of A number of nuclei of both are equal. Then the ratio NA/NB is

A

1/4

B

1/8

C

1/3

D

1/6

Answer

1/8

Explanation

Solution

Three half-lives of A is equivalent to six half-lives of B. Hence, NA(12)3\left( \frac { 1 } { 2 } \right) ^ { 3 }= NB (12)6\left( \frac { 1 } { 2 } \right) ^ { 6 }

or NANB\frac { N _ { A } } { N _ { B } } = 18\frac { 1 } { 8 }