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Half life of a radioactive sample is 2x ...

Half life of a radioactive sample is `2x` years. What fraction of this sample will remain undecayed after `x` years?

A

`(1)/(2)`

B

`(1)/(sqrt(2))`

C

`(1)/(sqrt(3))`

D

2

Text Solution

Verified by Experts

The correct Answer is:
b
`lambda = (2.303)/(t) log ((N_(0))/(N))`
`(0.693)/(t_(1//2)) = (2.303)/(t) log_(10) ((N_(0))/(N))`
`(0.639)/(2x) = (2.303)/(x) log_(10) ((N_(0))/(N))`
`(1)/(2) log_(10) 2 = log ((N_(0))/(N))`
`(N)/(N_(0)) = (1)/(sqrt(2))`
Fraction undecayed `= (1)/(sqrt(2))`
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