A radioactive sample has a half-life of 10 ~min . If 64 nuclei are contained in the sample the number of nuclei that would decay after, 50 ~min is

Step-by-step solution

Given, t_ 1 / 2 =10 ~min , N₀=64, t=50 ~min The number of half-lives in 50 ~min , n= t t_ 1 / 2 = 50 10 =5 In 5 half-lives, number of nuclei left undecayed, N=N₀ ( 1 2 )^ n =64 ( 1 2 )⁵= 64 32 =2 Number of nuclei decayed =N₀-N=64-2=62