Question

There are two radioactive substances A and B. Decay constant of B is two times that of A. Initially both have equal number of nuclei. After n half lives of A rate of disintegration of both are equal. The value of n is

• A. 1
• B. 2
• C. 4
• D. All of these

Answer 1

Answer: (A)

1

Answer 2

Let l_A = land l_B = 2l Initially rate of disintegration of A is l N₀ and that of B is 2l N₀. After one half-life of A, rate of disintegration of A will becomes $\frac { \lambda \mathrm { N } _ { 0 } } { 2 }$ and that of B would also be $\frac { \lambda \mathrm { N } _ { 0 } } { 2 }$ (half-life) of B = $\frac { 1 } { 2 }$ (half-life of A)

So, after one half-life of A or two half-lives of B.

$\left( - \frac { \mathrm { dN } } { \mathrm { dt } } \right) _ { \mathrm { A } }$ = $\left( - \frac { \mathrm { dN } } { \mathrm { dt } } \right) _ { B }$

\ n = 1