Some amount of a radioactice 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)=50 R` where `R= lambda N` since,
`R propN`
`(R )/(R _(0))=(N)/(N_(0))=((1)/(2))^(n)=((1)/(2))^(t//T)`or
`((1)/(2))^(t//10)=(1)/(50)`