Chapter 18, Problem 77QAP

Interpretation Introduction

(a)

Interpretation:

The amount of Pu-239 decomposed in 45 minutes in the following decay reaction needs to be calculated.

$\text{P}\text{u}\to \text{U}\text{ + }\text{H}\text{e}$

Concept introduction:

Radioactive decay follows first order kinetics as per the following relation:

$\begin{array}{l}\text{ln}\frac{\text{X}}{{\text{X}}_0}\text{ = kt ----(1)}\\ {\text{where, X}}_0=\text{ amount of radioactive substance at t = 0}\\ \text{X = amount of substance present at time t}\\ \text{k = decay constant}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The amount of energy released when $2.475\times {10}^{-9}g$ of Pu-239 decomposed in 45 min needs to be calculated

Concept introduction:

The energy change associated with a nuclear reaction is expressed as:

$\begin{array}{l}{\text{ΔE = Δmc}}^{\text{2}}\text{ ----(2)}\\ \text{where, }\Delta \text{m = change in mass = mass of prooducts - mass of reactants}\\ \text{c = speed of light }\end{array}$

Interpretation Introduction

(c)

Interpretation:

The radiation dose in rem received by a man weighing 75 kg and exposed to 1 g of Pu-239 for 45 min needs to be calculated.

Concept introduction:

The biological effect of radiation on tissues is expressed in terms of ‘rems’ i.e. radiation equivalent for man

$\begin{array}{l}1\text{ rem = n (no}\text{. of rads)}\\ \text{where n = factor that reflects the potential for damage by a particular radiation}\\ \text{n = 1 for beta and gamma emission}\end{array}$

$\begin{array}{l}\text{n = 20 for alpha}\\ {\text{1 rad = 10}}^{-2}\text{ J/kg}\end{array}$