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13.Nuclei
medium
The half life $(T)$ and the disintegration constant $(\lambda )$ of a radioactive substance are related as
A
$\lambda T = 1$
B
$\lambda T = 0.693$
C
$\frac{T}{\lambda } = 0.693$
D
$\frac{\lambda }{T} = 0.693$
Solution
(b) By using $N = {N_0}{e^{ – \lambda t}}$
==> $\frac{{{N_0}}}{2} = {N_0}{e^{ – \lambda \,{T_{1/2}}}}$
==> $2 = {e^{\lambda \,{T_{1/2}}}}$
By taking loge both the side
${\log _e}2 = \lambda {T_{1/2}}$ ==> $\lambda {T_{1/2}} = 0.693$
Standard 12
Physics
