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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))/(4)`
Decayed atoms `=N_(0)-N-N_(0)-(N_(0))/(4)=(3N_(0))/(4)`
`:.` Probabilty of decay `=(N_(0)-N)/(N_(0))=(3)/(4)`
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