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Chapter 32: Q8PE (page 1183)

What is the dose in mSv for: (a) a 0.1 Gy x-ray?

(b) 2.5 mGy of neutron exposure to the eye?

(c) 1.5 mGy of \(\alpha \) exposure?

Short Answer

Expert verified

a)The calculated dose in\(mSv\)for\(0.1\) Gy x-rayis\(100\,{\rm{mSv}}\).

b)The calculated dose in\(mSv\)of\(2.5\,{\rm{mGy}}\)of neutron exposure to the eye is \(80\,mSv\).

c) The calculated dose in \(mSv\) of \(1.5{\rm{m}}\,{\rm{Gy}}\) of \(\alpha \) exposure is \(15 - 30\,mSv\).

Step by step solution

01

Definition of Sievert unit

The Sievert symbol: is a derived unit of ionising radiation exposure in the International System of Units (SI) that is used to determine the health effects of low amounts of ionising radiation on the human body.

02

Calculating the dose in \({\bf{mSv}}\) for a \(0.1\) Gy x-ray

a)

Consider the given problem and solve.

According to the table\(32.2\), relative biological effectiveness (RBE) for\(X\)-rays is\(1\), so

\(\begin{aligned} {\rm{dose in Sv}} &= {\rm{Gy}} \times {\rm{RB}}\\ &= 0.1\;{\rm{Gy}} \cdot 1\\ &= 0.1\;{\rm{Sv}}\\ &= 100{\rm{mSv}}\end{aligned}\)

Therefore the calculated dose is \(100{\rm{mSv}}\).

03

Calculating the dose in \({\bf{mSv}}\) for \(2.5\,{\rm{mGy}}\) of neutron exposure to the eye

b)

Let us solve the given problem.

Neutrons have RBE on eyes of\(32,50\)

\(\begin{aligned} {\rm{dose in Sv}} &= {\rm{Gy}} \times {\rm{RBE}}\\ &= 2.5\,{\rm{mGy}} \cdot 32\\ &= 0.08\;{\rm{Sv}}\\ &= 80\,{\rm{mSv}}\end{aligned}\)

Therefore the calculated dose is \(80\,{\rm{mSv}}\).

04

Calculating the dose in \({\bf{mSv}}\) for \(1.5\,{\rm{mGy}}\) of \(\alpha \) exposure

c)

Calculate the dose in mSv.

\(\alpha \)particles have RBE from 10 to 20 , so

\(\begin{aligned} 1.5\,{\rm{mGy}} \cdot 10 & \le {\rm{ dose in Sv}} \le 1.5\,{\rm{mGy}} \cdot 20\\15\,{\rm{mSv}} &\le {\rm{ dose in Sv}} \le 30\,{\rm{mSv}}\end{aligned}\)

Therefore the calculated dose is \(15 - 30\)\(mSv\).

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