Some amount of a radioactive substance (half-life =10 days ) is spread inside a room and consequently the level of radiation become `50` times the permissible level for normal occupancy of the room. After how many days will the room be safe for occupation?.

Options

A. 20 days
B. 34.8 days
C. 56.4 days
D. 62.9 days

Answer

C

Explanation

Since, the initial activity is 50 times the activity for safe occupancy, therefore `R_(0)+ 50R`, where `R=lamda N`, Since, `R prop N`
`(R )/(R_(0)) = (N)/(N_(0)) = ((1)/(2))^(n)= ((1)/(2))^(t//T)` or `((1)/(2))^(t//10)= (1)/(50)`
`(2)^(t//10)=50 rArr (t)/(10) log_(10) 2=log_(10) 50`
`rArr t= (10 log_(10) 50)/(log_(10)^(2)) = (10 xx 1.699)/(0..301) =56.4` days