The radio iostope, tritium `(H^(3))` has a half life of 12:3 yr. If the initial amount of tritum is 32 mg, how many milligrams of it would remain after 49.2 yr?

Options

A. 4mg
B. 8 mg
C. 1 mg
D. 2 mg

Answer

D

Explanation

`t_(1//2)=12.3 yr`
Initial amount `(N_(0))=32 mg`
Amount left(N)=?
Total time (T)=49.2 yr
`(N)/(N_(0))=(1/2)^(n)`
where n=total number of half lives
`n=("Total time")/("Half life")=(49.2)/(12.3)=4`
so, `(n)/(N_(0))=(1/2)^(n)`
`(N)/(32)=(1/2)^(4)`
`(N)/(32)=(1)/(16)`
`N=(32)/(16)=2mg`