Question

Two radioactive X_(1) and X_(2) have decay constants 10 lambda and lambda respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei of X_(1) to that of X_(2)will be 1//e after a time .

Answer 1

The ratio between the number of nuclei of X1 and X2 will be t = 1 / 9 λ

Explanation:

Given data:

• Radio active element = X1 and X2
• Their wavelengths = 10 λ and λ

Solution:

Nx1(t) / Nx2(t) = 1e  

or N0 e^−10λt

N0 e^−λt = 1 e (Initially, both have same number of nuclei say N0)

or e^−9λt=e^−1

or e = e^9λt

or 9λt = 1 or

t = 1 / 9 λ

Hence the ratio between the number of nuclei of X1 and X2 will be t = 1 / 9 λ