A radioactive element X converts into another stable element Y . Half life of X is 2 hours. Initially only X is present. After a time t , if the ratio of atoms of X to Y is 1: 4 , then the value of t is

Step-by-step solution

Initially at t=0 , amount of X in sample =5 X After time ' t ' amount of X remained in sample =X From, N N₀ = ( 1 2 )^ t T We have, X 5 X = ( 1 2 )^ t 2 ( 1 2 )^ t 2 = 1 5 T=2 ~h As, 1 2^2 < 1 5 < 1 2^3 1 2^2 < 1 2^ t / 2 < 1 2^3 2 < t / 2 < 3 4 < t < 6