#### Question

The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively

##### Options

1/λ and (In 2/λ)

(In 2/λ) and 1/λ

λ(In 2) and 1/λ

λ/(In 2) and 1/λ.

#### Solution

(ln 2/λ) and 1/λ

The half-life of a radioactive sample `(t_(1"/"2))` is defined as the time elapsed before half the active nuclei decays.

Let the initial number of the active nuclei present in the sample be `N_0` .

`N_0/2 = N_0e^(-lambdat_"1/2")`

⇒ `t_"1/2" = ("In 2")/lambda`

Average life of the nuclei, `t_(av) = S/N_0 = 1/lambda`

Here, *S* is the sum of all the lives of all the *N* nuclei that were active at *t* = 0 and `lambda` is the decay constant of the sample.

Is there an error in this question or solution?

Solution The Decay Constant of a Radioactive Sample is λ. the Half-life and the Average-life of the Sample Are Respectively Concept: Radioactivity - Law of Radioactive Decay.