Question

Two radioactive materials Y₁ and Y₂ have decay constants '5`lambda`' and `lambda` respectively. Initially they have same number of nuclei. After time 't', the ratio of number of nuclei of Y₁ to that of Y₂ is `1/"e"`, then 't' is equal to ______.

Options

• `lambda/2`

• `"e"/lambda`

• `1/(4lamda)`

• `lambda`

Answer 1

Two radioactive materials Y₁ and Y₂ have decay constants '5`lambda`' and `lambda` respectively. Initially they have same number of nuclei. After time 't', the ratio of number of nuclei of Y₁ to that of Y₂ is `1/"e"`, then 't' is equal to `underline(1/(4lamda)`

Explanation:

` "N"_1 = "N"_0"e"^(-5lambda"t"),   "N"_2 = "N"_0"e"^(-lambda"t"`

`1/"e" = "e" ^(-lambda"t") = 1/"e"^(4lambda"t")`

`therefore 4lambda"t" = 1`

`therefore "t" = 1/(4lambda`