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

Answer 1

Answer: (B)

100 days

Answer 2

Let A be the activity for safe working.

Given Ao = 10 A Ao × No and A × N

$t = \frac{2.303}{\lambda}\log\frac{N_{0}}{N} = \frac{2.303}{\lambda}\log\frac{A_{0}}{A}$

$= \frac{\frac{2.303}{0.693}}{30}\log\frac{10A}{A} = \frac{2.303 \times 30}{0.693}\log 10 = \frac{2.303}{0.693} = 99.69days \approx 100days.$