Question

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

• A. $50days$
• B. $30days$
• C. $10days$
• D. $100days$

Answer 1

Answer: (A), (D)

$50days$
$100days$

Activity $\left(\frac{-d_N}{dt}\right)\propto N_t$

$N_t=N_0{\left(\frac{1}{2}\right)}^n$

$\frac{N_t}{N_0}={\left(\frac{1}{2}\right)}^n$

$\frac{1}{10}={\left(\frac{1}{2}\right)}^n$

$10=2^n$

$log10=nlog2$

$n=\frac{1}{0.301}=3.32$

$t=n\times t_{1/2}$

$3.32\times 30=99.6days\approx 100days\left(nearly\right)$