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13.Nuclei
medium
$t = 0$ સમયે એક્ટિવિટી $N_0$ છે. $t = 5$ મિનિટ એ એક્ટિવિટી $N_0/e$ છે. તો તત્વનો અર્ધઆયુ (મિનિટ)
A
${\log _e}\,2/5$
B
$\frac{5}{{{{\log }_e}\,2}}$
C
$5\,{\log _{10}}\,2$
D
$5\,{\log _e}\,2$
Solution
$N=N_{0} \mathrm{e}^{-\lambda t}$
Here, $t=5$ $minutes$
$\frac{N_{0}}{e}=N_{0} \cdot e^{-5 \lambda}$
$\Rightarrow \quad 5 \lambda=1,$ or $\quad \lambda=\frac{1}{5},$
Now, ${T_{1/2}} = \frac{{\ell n2}}{\lambda } = 5\ell n2$
Standard 12
Physics
