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:

  1. (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 $=4 \times 10^{16}-\frac{1}{2} \times 10^{16}$

$=3.5 \times 10^{16}$