If 50% of a radioactive substance dissociates in 15 min, then the time taken by substance to dissociate 99% will be

Options

A. 50 min
B. 100 min
C. 99 min
D. 150 min

Answer

C

Explanation

Radioactive disintegration is a first order reaction,
`k=(0.693)/(t_(1//2))=(0.693)/(15)" "(Given, t_(1//2)=15min)`
=0.0462
Given, a=100, x=99 t=?
`or" "0.0462=(2.303)/(t)"log"(100)/(100-99)`
`=(2.303)/(t)" log "100` `or" "0.0462xxt =2.303xx2`
`therefore" "t=(2.303xx2)/(0.0462)=99min`