Question

A radioactive element gets spilt 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. 1000 days
• B. 300 days
• C. 10 days
• D. 100 days

Answer 1

The correct option is D 100 days

We can solve this problem in 2 stages first we find out the "K" value from $t_{1/2}=\frac{0.693}{k_1}$ from this we get "K" as 0.0231.
Now putting this "K" in $k_1=\frac{2.303}{t}log\frac{a}{a-x}$ by putting value into equation we get $0.0231=\frac{2.303}{t}log\frac{10}{1}$
Now solving this we get
Ans: 100 days