Chapter 30, Problem 57P

To determine

A formula for the number of daughter nuclei $N_D$, as a function of time;

Answer to Problem 57P

Solution:

Number of daughter nuclei formed, $N_D=N_0(1-e^{-\lambda t})$

Explanation of Solution

Formula used:

The number of nuclei remaining after a time t, $N=N_0{e}^{-\lambda t}$, $N_0$ is the number of nuclei present after time t = 0 and $\lambda$ is the decay constant.

Calculation:

We have number of parent nuclei equation as $N=N_0{e}^{-\lambda t}$

$N_0$ is the number of nuclei present after time t = 0

Number of daughter nuclei formed after a time t, $N_D=N_0-N$

⇨ $N_D=N_0-N_0{e}^{-\lambda t}=N_0(1-e^{-\lambda t})$