Question

A sample of radioactive material decays simultaneously by two processes A and B with half lives 1/2 and 1/4 hr respectively. For first half hour it decays with the process A, next one hr with the process B and for further half an hour with both A and B. If originally there were N₀ nuclei, find the number of nuclei after 2 hr of such decay.

(A) N₀/(2)⁸

(B) N₀/(2)⁴

(C) N₀/(2)⁶

(D) N₀/(2)⁵

Answer 1

Correct answer is: (A) N₀/(2)⁸

After first half hrs  

N = N₀ 1/2

for t = 1/2 to t = 1 1/2

N = (N₀ 1/2) [ 1/2]⁴

= N₀ (1/2)⁵

for t = 1 1/2 to t = 2 hrs.

[for both A and B 1/t_1/2 = 1/1/2 + 1/1/4 = 2 + 4 =6 t_1/2 = 1/6 hrs.]

N = [N₀(1/2)⁵] (1/2)³ = N₀ (1/2)⁸