Two radioactive substance `A` and `B` have decay constants `5 lambda` and `lambda` respectively. At `t=0` they have the same number of nuclei. The ratio of number of nuclei of nuclei of `A` to those of `B` will be `(1/e)^(2)` after a time interval

Options

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

Answer

A

Explanation

`(N_(A))/(N_(B))=(N_(0)e^(-lambda_(A)t))/(N_(0)e^(-lambda_(B)t))=(e^(-5lambdat))/(e^(-lambdat))`
`implies (1)/(e^(4lambdat))=(1)/(e^(2))impliest=(1)/(2 lambda)`