The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a oe month old `P^32``(t_(1//2)=14.3` days) source if it was originally purchased for 800 rupees?

Answer

`Rs.182.8`

Explanation

Here, `T=14.3days, t=30 days`
`lambda=0.693/T=0.693/14.3day^(-1)`
As `A=A_(0)e^(-lambdat)`
`:. A/(A_(0))=e^((-30xx0.693)/14.3)=e^(-1.454)`
`log_(e).(A)/(A_(0))=-1.454 log_(e) e=-1.454`
`2.303 log_(10) .(A)/(A_(0))=-1.454`
`log_(10). (A)/(A_(0))=-1.454/2.303=-0.631=bar(1).369`
`A/(A_(0))=0.2285`
`:.` Sal e price =`0.2285xx800`
`=182.8 rupees`