Chapter 20, Problem 4SEPP

Interpretation Introduction

Interpretation:

The time required for the power to fall at $80\%$ of ${}^{\text{238}}\text{Pu}$ initial value is to be calculated.

Concept introduction:

The amount of a particular radioactive isotope left after time t is given as:

$\text{ln}\frac{N_t}{N_o}=-kt$

Here, $k$

is the rate constant for the radioactive decay, $N_t$ is the amount of sample left after time t, and $N_0$ is the initial amount of the sample.

The above formula can be modified in terms of power dissipated as:

$\text{ln}\frac{P_t}{P_o}\text{=}-kt$

Here, $k$

is the rate constant for the radioactive decay, $P_{\text{t}}$ is the power dissipated at time t, and $P_0$ is the power dissipated initially.