A radioactive element X converts into another stable element. Y half-life X is 2 h Initially only X is present. After time t, the ratio of atoms of X and Y is found to be `1:4` then t in hour is

Options

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

Answer

c

Explanation

Let `N_(2)` be the number of atoms of X at time `t =0`. Then, at `t=4h` (two half-lives),
`N_x =N_0/4` and `N_y =3N_0/4`
`because (N_(x))/(N_(y)) =(1)/(3) ~~0.33`
At `t=6th` (three half-lives), `N_(x) =(N_(0))/(8)` and `N_(y) =(7N_(0))/(8)` or `(N_(x))/(N_(y)) =(1)/(7) ~~0.142`
The given ratio `(1)/(4)` lies between `(1)/(3)` and `(1)/(7)`.
Therefore , t lies between `4 h` and `6h`.