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 permissibel value, after how many days will it be safe to enter the room?

Options

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

Answer

D

Explanation

Activity `(-(dN)/(dt)) prop N`
`N = N_0 (1/2)^n implies N/N_0 = (1/2)^n`
`1/(10) = (1/2)^n implies 10 = 2^n`
`log 10 = n log 2 `
`implies n = 1/(0.301) = 3.32 `
`t = n xx t_(1//2) = 3.32 xx 30 = 99.6 ` days