Question

Half-lives of two radioacitve substances A and Bare respectively 20 min and 40 min. Initially the samples of A and B have equal number of nuclei. After 80 min the ratio of remaining number of A and B nuclei is :

(A) 1 : 16 

(B) 4 : 1

(C) 1 : 4 

(D) 1 : 1

Answer 1

Correct Answer is: (C) 1 : 4 

Key Idea :Total no. of nuclei remained after n 

half-lives is N = N₀ (1/2)ⁿ. 

Total time given = 80 min Number of half-lives of A, n_A = 80 min/ 20 min = 4

Number of half-lives of B, n_B = 80 min/ 40 min = 2

Number of nuclei remained undecayed N =  N₀ (1/2)ⁿ where N₀ is initial number of nuclei

NOTE : The graph between number of nuclei decayed with time is shown along side,