Question

A radioactive element gets spilled over the floor of a room. Its half life period is $30$ days. If initial rate is ten times the permissible value, after how many days will it be safe to enter the room?

• A. $100$ days
• B. $1000$ days
• C. $300$ days
• D. $10$ days

Answer 1

The correct option is A $100$ days

$\cdot$> It will be safe to enter the room after the nuclei decreases to $\frac{1}{10}$ of its initial amount.

$⟶$Half life = 30 days

$t_{1/2}=\frac{0.693}{\lambda }$

$\Rightarrow \lambda =\frac{0.693}{30}{day}^{-1}$

$⟶$Using integration law,

$\lambda t=ln\left(\frac{N_o}{N_t}\right)$

$t=\frac{30}{0.693}ln\left[\frac{N_o}{1/10N_o}\right]\Rightarrow \frac{30}{0.693}\times ln10.$

$t=100days.$

$\therefore$After 100 days, it will be safe to enter the room.