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 ?

Options

A. `underline~`1000 days
B. `underline~`300 days
C. `underline~`10 days
D. `underline~`100 days

Answer

d

Explanation

It will be safe to enter in the room when activity gets reduces by 10 times, i.e, when N=`N""_(0)//10`
`therefore N""_(0)/N=((1)/(2))""^(n)or1/10=(1/2)""^(n)`
`or10=2""^(n)` log10=nlog2
`n=1/0.301=3.32 t=nlog2`
`=3.32xx30=99.6 days`