Two radioactive materials `X_(1)` and `X_(2)` have decay constants `5 lambda` and `lambda` respectively. If initially they have the same number of nuclei, then the ratio of the number of muclei of `X_(1)` to that of `X_(2)` will be `1/e` after a time

Options

A. `lamda`
B. `(1)/(2)lamda`
C. `(1)/(4lamda)`
D. `(e)/(lamda)`

Answer

C

Explanation

Number of atoms remained undecayed after time
t, `N=N_(0)e^(-lamdat)`
Given, `N=(3N_(0))/(100)`
`therefore (3N_(0))/(100)=N_(0)e^(-lamdat) or 3=100e^(-lamdat)` . . (i)
Now, `lamda=(0.693)/(T_(1//2))=(0.693)/(2)=0.346`
Substituting the value of `lamda` in Eq. (i), we get
`2.303log((3)/(100))=-0.346t`
`-1.52xx2.303=-0.346t implies t=10`yr