Nuclei - Result Question 82
84. The decay constant $(\lambda)$ and the half-life (T) of a radioactive isotope are related as
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(a) $\lambda=\frac{\log _{e} 2}{T}$
(b) $\lambda=\frac{1}{\log _{e} 2 . T}$
(c) $\lambda=\frac{T}{\log _{e} 2}$
(d) $\lambda=\frac{2}{T}$
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Answer:
Correct Answer: 84. (a)
Solution:
- (a) $t=\frac{1}{\lambda} \log \frac{a}{a-x} \quad$ when $t=T, x=\frac{a}{2}$
$T=\frac{1}{\lambda} \log \frac{a}{a-\frac{a}{2}}=\frac{1}{\lambda} \log _{e} 2 \Rightarrow \lambda=\frac{1}{T} \log _{e} 2$
