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The radio iostope, tritium (H^(3)) has a...

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?

A

(a) 4mg

B

(b) 8 mg

C

(c) 1 mg

D

(d) 2 mg

Text Solution

Verified by Experts

The correct Answer is:
D
`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`
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