MCQ
The mean life time of a radionuclide, if its activity decrease by $4\%$ for every $1h$ , would be .......... $h$ [product is non-radioactive i.e. stable]
- ✓$25$
- B$1.042$
- C$2$
- D$30$
✓
Answer
Correct option: A.
$25$
a
$\frac{\mathrm{dN}}{\mathrm{dt}}=\frac{0.04 \mathrm{N}}{3600}$ (given)
$\frac{\mathrm{dN}}{\mathrm{dt}}=\frac{0.04 \mathrm{N}}{3600}$ (given)
But $\frac{\mathrm{d} \mathrm{N}}{\mathrm{dt}}=-\lambda \mathrm{N}$
So $-\lambda N=\frac{-0.04}{3600} \mathrm{N}$ or $\lambda=\frac{0.04}{3600} \mathrm{\,s}^{-1}$
Mean life $T=\frac{1}{\lambda}=\frac{3600}{0.04} s=25\, h$
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