Chapter 24: Q24.62 P (page 1104)

A $70$ .-kg person exposed to $90$ Sr absorbs ${6x10}^{5} β$ particles, each with an nergy of ${8.74x10}^{-14}$ J.
(a) How many grays does the person receive?
(b) If the RBE is $1.0$ , how many millirems is this?
(c) What is the equivalent dose in sieverts (Sv)?

Short Answer

Expert verified

$\begin{array}{l} {a.7.4914x10}^{-10} Gy \\ {b.7.4914x10}^{-5} mrem \\ {c.7.4914x10}^{-10} Sv \end{array}$

Step by step solution

Introduction

The SI unit of such energy absorption is the gray (Gy) which is equal to $1 \frac{J}{kg}$ of body tissue. A more widely used unit is the rad (radiation-absorbed dose), which is one-hundredth as much:

_{$1rad= \frac{0.01.J}{kg} =0.01Gy$}

To find millirems, we need to convert Gy to rads. Also, in order to find rems, we must multiply rads by the given RBE. Then we just have to convert rems to mrem.

To convert the dose to sieverts, we need to note that,

_{$1rem=0.01Sv$}

Calculation

a. Absorbed Energy (J)

_{$\begin{array}{l} ({6x10}^{5} β) ({8.74x10}^{-14} \frac{J}{β}) {=5.244×10}^{-8} J \frac{{5.244x10}^{-8} .J}{70kg} (\frac{1rad}{\frac{0.01,J}{kg}}) (\frac{0.01Gy}{1rad}) \\ {=7.4914×10}^{-10} Gy \end{array}$}

b. mrem

Remember that the given RBE is 1 .

Therefore,

_{${7.4914x10}^{-10} Gy (\frac{1rad}{0.01Gy}) (1) (\frac{1mrem}{10^{-3} rem}) {=7.4914x10}^{-5} mrem$}

c. Dose (Sv)

_{${7.4914x10}^{-5} mrem (\frac{10^{-3}}{1mrem}) (\frac{0.01Sv}{1rem}) {=7.4914x10}^{-10} Sv$}

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A $70$ .-kg person exposed to $90$ Sr absorbs ${6x10}^{5} β$ particles, each with an nergy of ${8.74x10}^{-14}$ J.
(a) How many grays does the person receive?
(b) If the RBE is $1.0$ , how many millirems is this?
(c) What is the equivalent dose in sieverts (Sv)?

Short Answer

Step by step solution

Introduction

Calculation

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A 70.-kg person exposed to90 Sr absorbs 6x105βparticles, each with an nergy of8.74x10-14 J.(a) How many grays does the person receive?(b) If the RBE is1.0 , how many millirems is this?(c) What is the equivalent dose in sieverts (Sv)?

Short Answer

Step by step solution

Introduction

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Physical Chemistry

Making Measurements

Chemical Analysis

The Earths Atmosphere

Nuclear Chemistry

Study anywhere. Anytime. Across all devices.

A $70$ .-kg person exposed to $90$ Sr absorbs ${6x10}^{5} β$ particles, each with an nergy of ${8.74x10}^{-14}$ J.
(a) How many grays does the person receive?
(b) If the RBE is $1.0$ , how many millirems is this?
(c) What is the equivalent dose in sieverts (Sv)?