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The half-life of a sample of a radioacti...

The half-life of a sample of a radioactive substance is `1` hour. If `8 xx 10^10` atoms are present at `t = 0`, then the number of atoms decayed in the duration `t = 2` hour to `t = 4` hour will be

A

`2 xx 10^(10)`

B

`1.5 xx 10^(10)`

C

zero

D

infinity

Text Solution

Verified by Experts

The correct Answer is:
B
Since, `(N)/(N_(0))= ((1)/(2))^(t//T_(1//2))`
At t= 2 hr
`N_(1)= 8 xx 10^(10) ((1)/(2))^((2)/(1)) = 2 xx 10^(10)`
At t= 4hr
`N_(2)= 8 xx 10^(10) ((1)/(2))^((4)/(1)) = (1)/(2) xx 10^(10)`
Number of decayed atom in that duration
`=(2- (1)/(2)) xx 10^(10) = 1.5 xx 10^(10)`
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