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The half life of a radioactive element ...

The half life of a radioactive element is 30 min. One sixteenth of the original quantity of element will be left after
a. 1 hr b. 16 hr c. 4 hr d. 2 hr

A

a. 1 hr

B

b. 16 hr

C

c. 4 hr

D

d. 2 hr

Text Solution

Verified by Experts

The correct Answer is:
d. 2 hr
Given `t_(1//2) = 30` min or `(1)/(2) hr`
`(N)/(N_(0)) = (1)/(16)`
We have `(N)/(N_(0)) = ((1)/(2))^(n) implies ((1)/(16)) = ((1)/(2))^(n)`
`((1)/(2))^(4) = ((1)/(2))^(n) implies 2 = 4`
`T = n xx t_(1//2) = 4 xx (1)/(2) = 2 hr`
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