Given that radioactive species decays according to the exponential law `N=N_(0) e^(-lambda t)`. The half life of the species is

Options

A. `lambda`
B. `N_(0)`
C. `lambda//ln//2`
D. `ln 2//lambda`

Answer

D

Explanation

`N=N_(0)e^(-lambdal)`
`(N_(0))/(N)=e^(lambda l)`
When `t=t_(1//2), N_(0)/N=2`
`2=e^(lambda t_(1//2))`
`"log"_(e)2=lambda t_(1//2)`
`t_(1//2)=("log"_(e)2)/(lambda)=("In" 2)/(lambda)`