A radioactive element` X` converts into another stable elemnet `Y`. Half-life of `X` is `2h`. Initally, only `X` is present. After time `t`, the ratio of atoms of `X` and `Y` is found to be `1:4` Then `t` in hours 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 = 4hrs (two half lives)
`N_(x)=(N_(0))/(4)` and `N_(y)=(3N_(0))/(4)`
`:. N_(x)//N_(y)=1//3` and at t = 6 hrs (three half lives)
`N_(x)=(N_(0))/(8)`and `N_(y)=(7N_(0))/(8)` or `(N_(x))/(N_(y))=(1)/(7)`
The given ratio `(1)/(4)` lies between `(1)/(3)` and `(1)/(7)` therefore, t lies between 4 hrs and 6 hrs.