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13.Nuclei
hard
Half-life of a radioactive substance is $20\,minute$ . The time between $20\%$ and $80\%$ decay will be ......... $min$
A
$20$
B
$40$
C
$30$
D
$25$
(AIIMS-1999)
Solution
$\mathrm{t}_{1 / 2}=20 \mathrm{min}$
$\lambda=\frac{\ell \mathrm{n} 2}{20}$
$\frac{0.8 \mathrm{N}_{0}=\mathrm{N}_{0} \mathrm{e}^{-\lambda t_{1}}}{0.2 \mathrm{N}_{0}=\mathrm{N}_{0} \mathrm{e}^{-\lambda\left(t_{2}\right)}}$
$4=e^{+\lambda\left(t_{2}-t_{1}\right)}$
$\ln 4=\lambda\left(t_{2}-t_{1}\right)$
$\left(t_{2}-t_{1}\right)=40 \mathrm{\,min}$
Standard 12
Physics
