A radioactive sample undergoes decay as per the following gragp. At time` t=0`, the number of undecayed nuclei is `N_(0)`. Calculate the number of nuclei left after `1 h`.
.

Options

A. `N_(0)//e^(8)`
B. `N_(0)//e^(10)`
C. `N_(0)//e^(12)`
D. `N_(0)//e^(14)`

Answer

c

Explanation

`t=0,N=N_(0)`
`t=6.93,N=N_(0)//4`
`N_(0)//4` is the sample left after two half-lives
`:. 2 t_(1//2)=6.93`
`rArr 2 xx( 90.693)/(lambda) f=6.93 rArr lambda =0.2 min^(-1)`
`rArr t=60 min`
`:. N=N_(0) e^(-lambda t) =N_(0) e^(-02xx60)=(N_(0))/(e^(12))`.