Two radioactive material `A_(1)` and `A_(2)` have decay constants of 10 `lambda_(0)` and `lambda_(0)`. If initially they have same number of nuclei, then after time `(1)/(9 lambda_(0)) ` the ratio of number of their undecayed nuclei will be

Options

A. `(1)/(e)`
B. `(1)/(e^(2))`
C. `(1)/(e^(3))`
D. `(sqrt(e))/(1)`

Answer

A

Explanation

`A_(1) overset(10lambda_(0))rarrX`Initial no. of nuclei `=N_(0)`
`A_(2) overset(lambda_(0))rarrY`Initial no. of nuclei=`N_(0)`
For `A_(1)`
No. of nuclei left undecayed after time `(1)/(9 lambda_(0))=N_(0)e^(-10lambda_(0)xx(1)/(9 lambda_(0)))=N_(0)e^(-(0)/(9))`
For `A_(2)`
No. of nuclei left undercayed after time `(1)/(9lambda_(0))=N_(0)e^(-lambda_(0)xx(1)/(9lambda_(0)))=N_(0)e^(-(1)/(9))`
Radio `(N_(0)e^(-(10)/(9)))/(N_(0)e^(-(1)/(9)))=e^(-1)=(1)/(e)`