If time t is required for a radioactive substance to become one third of its initial amount, what fraction would be left after 0.5 t ?

Options

A. `(1)/(sqrt(3))`
B. `(1)/(2)`
C. `(1)/(3)`
D. `sqrt((2)/(3))`

Answer

a

Explanation

`lambda = (2.303)/(t) log ((N_(0))/(N))`
`(N)/(N_(0)) = (1)/(3)` in time 't
`:. lambda = (2.303)/(t) log_(10) 3`
After 0.5 t time:
`lambda = (2.303)/(0.5t) log ((N_(0))/(N))`
Equationg (i) and (ii) we get
`(N)/(N_(0)) = (1)/(sqrt(3))`