NEET-XII-Physics
46: The Nucleus
- #15The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively
(a) 1/λ and (In 2/λ)
(b) (In 2/λ) and 1/λ
(c) λ(In 2) and 1/λ
(d) λ/(In 2) and 1/λ.digAnsr: bAns : (b) (ln 2/λ) and 1/λ
The half-life of a radioactive sample (`` {t}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}``) 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 N0.
`` \frac{{N}_{o}}{2}={N}_{o}{e}^{-\lambda {t}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}``
`` \Rightarrow {t}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{\,\mathrm{\,ln\,}2}{\lambda }``
Average life of the nuclei, `` {t}_{av}=\frac{S}{{N}_{o}}=\frac{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.
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