Nuclei - Result Question 80
81. A sample of radioactive element has a mass of $10 gm$ at an instant $t=0$. The approximate mass of this element in the sample after two mean lives is
[2003]
(a) $6.30 gm$
(b) $1.35 gm$
(c) $2.50 gm$
(d) $3.70 gm$
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Answer:
Correct Answer: 81. (b)
Solution:
- (b) Using the relation for mean life.
Given : $t=2 \tau=2(\frac{1}{\lambda}) \quad(\therefore \tau=\frac{1}{\lambda})$
Then from $M=M_0 e^{-\lambda_t}=10 e^{-\lambda \times \frac{2}{\lambda}}$
$=10(\frac{1}{e})^{2}=1.35 g$
The law of radioactive disintegration in terms of mass can be written as
$M=M_0 e^{-\lambda t}$
Here, $M_0=$ mass of radioactive nuclei at time $t=0$ $M=$ mass of radioactive nuclei at time $t$
82
(d) $N=4 \times 10^{16}(\frac{1}{2})^{\frac{30}{10}}=\frac{1}{2} \times 10^{16}$
Atoms decayed $=4 \times 10^{16}-\frac{1}{2} \times 10^{16}$
$=3.5 \times 10^{16}$
