Question

If t is the time required for a radioactive substance to reduce to one third of its initial amount, what fraction would be left over after0.5 t

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{\frac{2}{3}}$

Answer 1

The correct option is C

$\frac{1}{\sqrt{3}}$

$t=\frac{1}{\lambda }In\frac{N_0}{N}=\frac{1}{\lambda }in\frac{1}{\frac{1}{3}}=\frac{1}{\lambda }In3$ ....(i)
and $0.5t=\frac{1}{\lambda }In\frac{1}{x}$ (x fraction left) .....(ii)
From (i) and (ii) $x=\frac{1}{\sqrt{3}}$