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After 24 hour, only 0.125" g" out of the...

After 24 hour, only `0.125" g"` out of the initial quantity of 1 g of a radioactive isotope remains behind. The half-life period of the radioactive isotope in hours is

A

`7.2 h`

B

`7.99 h`

C

`6.99 h`

D

`10.0 h`

Text Solution

Verified by Experts

The correct Answer is:
B
In this problem , 'a'=1.0g and 'a-x'=0.125g and 't'=24h. Therefore, the disintegration constant.
`lambda= (2.303)/(t) "log" (a)/(a-x)`
Or `lambda =(2.303)/(24)"log" (1)/(0.125)=0.0866h^(-1) " "` Or `" " t_(1//2)=(0.693)/(0.0866)=7.99` hours
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