To investigate the beta-decay of `Mg^(23)` radionuclide, a counter was activated at the moment `t=0`. It registered `N_(1)` beta particles by a moment `t_(1)=2 sec`, and by a moment `t_(2)=3t_(1)` the number of registered beta particles was `2.66` times greater. the mean life of the given nuclei is

Options

A. `3 sec`
B. `7 sec`
C. `16 sec`
D. `14 sec`

Answer

C

Explanation

`Mg^(23)` give one `beta`-particle in one disintergration. Number of `beta`-particle `=` number if decayed nuclei `=` number of disintergrations`=N_(0)(1-e^(-lambda t))`
`:. N_(0)(1-e^(-lambda t))=N_(1) &`
`N_(0)(1-e^(- lambda t_(2)))=N_(2)=2.66N_(1), 3t_(1)`
after simplification `e^(-2 lambda)=0.882, rArr(1)/(lambda)= tau=16 sec`