Half-lives of two radioactive elements A and B are 30 minute and 60 minute respectively. Initially the samples have equal number of nuclei. After 120 minute the ratio of decayed numbers of nuclei of B to that of A will be

Step-by-step solution

For radioactive decay, amount of sample remaining is given by, N = N _ o ( 1 2 )^ _o is initial sample and is decay constant. Decay constant, = ( t t _ 1 / 2 )= 120 t _ 1 / 2 ... (given) For element A, N _ A = N _ o ( 1 2 )^ 120 30 = N _ o 2^4 ...[From(i)] Amount of sample A decayed, N_A^ =N_o-N_A=N_o- N₀ 2^4 = 15 16 N₀...(i) For element B, N _ B = N _ o ( 1 2 )^ 120 60 = N ₀ 2^2 ..[From(i)] Amount of sample B decayed, N _ B ^ = N _ o - N _ B = N _ o - N _ o 2^2 = 3 4 ~N _ O ...(iii) From (ii) and (iii),