A radioactive element gets spilled over the floor of a room, Its half-life period is 30 days. If the initial activity is 10 times the permissible value, after how many days will it be safe to enter the room ?

Options

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

Answer

A

Explanation

We know that Activity ` = (-(dN)/(dt)) prop N, N = N_(0) ((1)/(2))^(n) rArr (N)/(N_(0)) = ((1)/(2))^(n)`
Therefore, `(1)/(10) = ((1)/(2))^(n) rArr 10 = 2^(n)`. Taking log on both sides, we get log 10 = n log 2 of `n =(1)/(0.301) = 3.32` (as log 2 = 0.3010). Therefore,` t = n xx t_(1//2) = 3.32 xx 30 = 99.6` days