The half life of `Tc^(99)` is `6.0 hr`. The delivery of a sample of `Tc^(99)` from the reactor to the nuclear medicine lab of a certain hospital takes `3.0 hr`. What is the minimum amount of `Tc^(99)` that must be shipped in order for the lab to receive `10.0 mg` ?

Options

A. `20.0 mg`
B. `15.0 mg`
C. `14.1 mg`
D. `12.5 mg`

Answer

C

Explanation

`t1//2=6` hour ` " " l=(0.693)/(6) "hour"^ (-1)`
`lambda=(l)/(t) ln (N_(0))/(N) rArr (0.693)/(6) =(l)/(3) ln ((x)/(10)) " " x rarr "initial amount of " Tc^(99)`
`(x)/(10)=e^((0.693)/(6))`
`x=14.1 mg`