Answered: One of the hazards of nuclear…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter14: Nuclear Physics Applications

Section: Chapter Questions

Problem 17P

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Question

One of the hazards of nuclear explosions is the generation of ⁹⁰Sr and its subsequent incorporation in place of calcium in bones. This nucl ide emits β particles of energy 0.55 MeV. and has a half-l ife of 28.1 a. Suppose 1.00 μg was absorbed by a newly born ch ild. How much will remain after
(a) 19 a, (b) 75 a if none is lost metabolica lly?

Expert Solution

Step 1

Given:

The half life is t=28.1 years.
The energy is E=0.55 MeV.
The amount radioactive material of N'=1 μg.
The time is T=19 years.

(a)

The expression of half life is given by,

$λ = \frac{0.693}{t} λ = \frac{0.693}{28.1} λ = 0.024 m$

The expression of nuclear decay is given by,

$T = \frac{2.303}{λ} \log (\frac{N'}{N})$

Substitute the values in the above expression.

$\begin{array}{rcl} 19 years & = & \frac{2.303}{0.024 m} \log (\frac{1 \times 10^{- 6} g}{N}) \\ \log (\frac{1 \times 10^{- 6} g}{N}) & = & 0.198 \\ N & = & 8.21 \times 10^{- 7} g \end{array}$

Thus, the remaining amount is $\begin{array}{rcl} N \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} 8 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 21 \end{array} \begin{array}{rcl} \times \end{array} \begin{array}{rcl} 10 \end{array} \begin{array}{rcl} ^{- 7} \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} g \end{array}$ .

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