Question

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

Answer 1

Correct Answer - 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))`