# The Decay Constant of a Radioactive Sample is λ. the Half-life and the Average-life of the Sample Are Respectively - Physics

MCQ

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.

Concept: Radioactivity - Law of Radioactive Decay
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 24 The Nucleus
MCQ | Q 15 | Page 441