Question

If $N_t=N_0{e}^{-\lambda t}$ then number of disintegrated atoms between $t_1$ to $t_2$ ($t_2>t_1$) will be:

• A. $N_0[e^{\lambda t_2}-e^{\lambda t_1}]$
• B. $N_0[-e^{\lambda t_2}-e^{-\lambda t_1}]$
• C. $N_0[e^{-\lambda t_1}-e^{-\lambda t_2}]$
• D. none

Answer 1

The correct option is C $N_0[e^{-\lambda t_1}-e^{-\lambda t_2}]$

Initial amount is $N_0$ so amount after time $t_1$ will be $N=N_0{e}^{-\lambda t_1}$

And that after time $t_2$ is $N_2=N_0{e}^{-\lambda t_2}$

So decayed in period between $t_1$ and $t_2$ is nothing but $N_1-N_2=N_0(e^{-\lambda t_1}-e^{-\lambda t_2})$ as $N_1>N_2$

option c is correct.