Half-lives of two radioactive substances A and B are 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

Step-by-step solution

Key Idea : Total number 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 remains undecayed N=N₀ ( 1 2 )^n where N₀ is initial number of nuclei. array ll & N_A N_B = ( 1 2 )^ n_A ( 1 2 )^ n_B or & N_A N_B = ( 1 2 )^4 ( 1 2 )^2 = ( 1 16 ) ( 1 4 ) or & N_A N_B = 1 4 array