Question

A sample of a radioactive element has a mass of 10 g at an instant t = 0 the approximate mass of this element in the sample left after two mean lives is.

• A. $1.35g$
• B. $2.50g$
• C. $3.70g$
• D. $6.30g$

Answer 1

Answer: (A)

$1.35g$

Answer 2

: Here $t = 2\tau = 2 \times 1.44T_{1/2} = 2.88T_{1/2}$

As $\frac{N}{N_{0}} = \frac{m}{m_{0}} = \left( \frac{1}{2} \right)^{t/T_{1/2}} = \left( \frac{1}{2} \right)^{2.88}$

$\therefore m = n_{0}\left( \frac{1}{2} \right)^{2.88} = 10\left( \frac{1}{2} \right)^{2.88}g = 10 \times 0.1358g = 1.358g$