Question

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life $18$ days inside the laboratory. Tests revealed that the radiation was $64$ times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

• A. $64$
• B. $90$
• C. $108$
• D. $120$

Answer 1

Answer: (C)

$108$

Given : $T_{1/2}=18$ days

Let the permissible activity after time $t$ be $R_o$

$⟹$ Initial activity of the radiation, $R=64R_o$

Using : $\frac{0.693}{T_{1/2}}t=2.303{\log }_{10}\frac{R}{R_o}$

$\therefore$ $\frac{0.693}{18}t=2.303{\log }_{10}\left(64\right)$

$\frac{0.693}{18}t=2.303\times 1.806$ $⟹t=108$ days