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(87)^(221) Ra is a radioactive substance...

`_(87)^(221) `Ra is a radioactive substance having half life of `4` days .Find the probability that a nucleus undergoes decay after two half lives

A

1

B

`1//2`

C

`1//4`

D

`3//4`

Text Solution

Verified by Experts

The correct Answer is:
D
`n = (t)/( t _(1//2)) = 8/4 =2`
`N _(0) = 2 ^(n) N, (N _(0))/( N) = 2 ^(2) =4`
Remaining atoms `= N = (N_(0))/(N)`
Dacayed atoms
`= N_(0) - N = N _(0) - (N_(0))/(4) = (3 N _(0))/(4)`
`therefore `Probability of decay `= (N_(0) - N )/( N _(0)) =3/4`
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