Question

A completely air tight container contains $100$grams of radioactive material.After $24$days, only $12.5$ grams of radioactive material left in the bottle.Calculate the half-life of this radioactive material?

• A. 24 days
• B. 16 days
• C. 12 days
• D. 8 days
• E. 3 days

Answer 1

The correct option is D 8 days

Given : $R_o=100$ grams, $R=12.5$ grams, $t=24$ days

Using : $\frac{0.693}{T_{1/2}}t=\ln \frac{R}{R_o}$

$\therefore$ $\frac{0.693}{T_{1/2}}\times 24=\ln \frac{100}{12.5}=\ln 8$ $(\ln 8=2.079)$

$\frac{0.693}{T_{1/2}}\times 24=2.079$ $⟹T_{1/2}=8$ days