Question

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

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

Answer 1

Answer: (D)

$100days$

Let permissible value = x
Thus activity = 10x
And $\lambda$(decay constant) = $\frac{0.693}{t_{1/2}}$

By first order reaction
$⟹kt=2.303\log \frac{10x}{x}$
$⟹t=\frac{2.303}{0.693}\times 30\log 10$

Solving this we get t = 100 days