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

Options

A. 2 hours
B. 4 hours
C. between 4 hours and 6 hours
D. 6 hours

Answer

C

Explanation

`X overset(2"hours") rarr Y` Initially at t = 0 amount of X in sample = 5X
After time t amount of X remained in sample = X
From `(N)/(N_(0))= ((1)/(2))^(t/T)`
We have `(X)/(5X) = ((1)/(2))^(t/2) implies ((1)/(2))^(t/2)= (1)/(5)`
`:. T = 2h`
As `(1)/(2^(2)) lt (1)/(5) lt (1)/(2^(3)) implies (1)/(2^(2)) lt (1)/(2^(t//2)) lt (1)/(2^(3))`
`2lt t//2lt 3 implies 4 lt t lt 6`