A human body excreates (removes by waste discharge, sweating, etc,) certain materials by a law similar to radioactivity.If technitium is injected in some form in 24 hours.a patient is given an injection containing ``^99Tc`.This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is `6 mu Ci`. How much time will elapse before the activity falls to `3 mu Ci`?

Answer

D

Explanation

Given, `t_1 = 24 h, t_2 = 6h`
`:. t_(1/2) = (t_1t_2)/(t_1 + t_2) = (24 xx 6)/(24 + 6)`
`= (24 xx 6)/30 = 4.8h`
Given `A_0 = 6muCi, A = 3muCi`
`:. A = A_0/(2^(t//t_2))`
`rArr 3muCi = (6 muCi)/(2^(t//4.8)`
`rArr (6muCi)/(2^(t//4.8)) = 3 rArr t/(4.8h) = 1`
` rArr t = 4.8h`.