The activity of a radioactive sample falls from `600 s^(-1) to 500 s^(-1) in 40 minutes. Calculate its half-life.

Answer

`152mi n`

Explanation

form `A=A_(0)e^(-lambdat)`
`500=600e^(-lambdat)`
`e^(lambdat)=600/500`
`lambdat log_(e) e=log_(e) (6//5)`
`lambda=(log_(e) (6//5))/t`
Half life, `T=0.693/(lamdba)=(0.693xxt)/(log_(e) (6//5))`
`T=(0.693xx40)/(2.303xx0.792)=152min`