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Two radioactive materials Y_{1} and Y_{2} 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 Y_{1} to that of Y_{2 }is `1/"e"`, then 't' is equal to ______.

#### Options

`lambda/2`

`"e"/lambda`

`1/(4lamda)`

`lambda`

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#### Solution

Two radioactive materials Y_{1} and Y_{2} 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 Y_{1} to that of Y_{2 }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`

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