90% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initial sample will decay in a total time 2t

Options

A. `20%`
B. `19%`
C. `40%`
D. `38%`

Answer

b

Explanation

`90%` of the sample is left undecayed after time t.
`:. (9)/(10) N_(0) =N_(0) e^(-lambda t)`
`lambda =(1)/(t) In(10)/(9)`
After time `2t`, (i)
`N_(C) =N_(0) e^(- lambda (2t)) =N_(0) e^((-1)/(t)[1n(10)/(9)]2t)` (ii)
`N=N_(0)e^(-In((10)/(9))^(2)=No((9)/(10))^(2)~~81%` of `N_(0)` (iii)
Therefore, `19% `of initial value will decay in time `2 t.