Chapter 30
X Rays
GOALS
When you have mastered the material in this chapter, you will be able to:
Definitions
Define each of the following terms, and use it in an operational definition:
hard and soft x rays
Bremsstrahlung
characteristic x rays
absorption coefficient
X-ray Problems
Solve problems involving the generation, absorption, and detection of x rays.
X-ray Interactions
List and discuss the interactions of x rays with matter- particularly those with
humans.
PREREQUISITES
Before beginning this chapter you should have achieved the goals of Chapter 21,
Electrical Properties of Matter, Chapter 27, Quantum and Relativistic Physics,
and Chapter 28, Atomic Physics.
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Chapter 30
X Rays
OVERVIEW
When high speed electrons (greater than 10,000 eV) strike a solid target (e.g.,
copper) high energy, short wavelength photons are produced. These photons are
called "x rays." Because of their high energy, x rays have remarkable penetrating
power. In this chapter you will read about the production, absorption, and detection
of x rays. Also, because x rays can produce damage to biological tissue, the
biological effects of x rays will be discussed.
SUGGESTED STUDY PROCEDURE
Before you begin your study of this chapter, be familiar with the following
Chapter Goals: Definitions, X-Ray Problems, and X-Ray Interactions. An extended
discussion of each of the terms listed under the Definitions goal are included in the
first section of this Study Guide chapter.
Next, read chapter sections 30.1-30.9. As you read please keep in mind that X
rays are not electrons, but high-energy photons. Thus, from the photon theory, x
rays have both particle and wave characteristics. Also, be cautious of equation 30.3.
If you do not recognize the exponential nature of the equation, look at Appendix,
Section A9.
Now turn to the end of the chapter and read the Chapter Summary and complete
Summary Exercises 1-9. Now, do Algorithmic Problems 1-3 and Exercises and
Problems 1-3, 5, 6, 11-14, and 16. Be sure that you compare your answers to each of
these problems to those given. If you need assistance with any part, turn back to a
portion of the text or to this Study Guide chapter. This study procedure is outlined
below.
--------------------------------------------------------------------------------------------------------------------Chapter Goals
Suggested
Summary
Algorithmic
Exercises
Text Readings Exercises
Problems
& Problems
--------------------------------------------------------------------------------------------------------------------Definitions
30.1,30.2,30.6
1,2,3,
14, 16
30.7,30.8
4,5,6
X-Ray
Problems
30.2,30.8
7,8
X-Ray
Interactions
30.3,30.4,30.5
9
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1,2,3,
1,2,3,
5, 6
11,12,13
DEFINITIONS
HARD X RAYS - The higher energy and greater penetrating x rays.
SOFT X RAYS - The lower energy and lesser penetrating x rays.
BREMSSTRAHLUNG - "Break radiation" is the name given to the continuous x-ray
spectrum from an x-ray source.
In most medical uses of x rays a metal plate such as an aluminum disc is used to
absorb the low energy Bremsstrahlung radiation as it leaves the x- ray tube.
CHARACTERISTIC X RAYS - The x ray production due to inner electron energy state
transitions that result in x-ray photons.
The inner electron energy shells are often labeled by the letters K, L, M, N, ...
instead of the value of the principle quantum number n = 1, 2, 3, 4, ... respectively.
Thus the various characteristic x-rays are sometimes labeled by the final state of the
electron after x-ray production, such as Kα where the K means the final state of the
electron is the K or n=1 state and alpha means the electron originated at the first
level above K, i.e. the L or n=2 state. Hence, when an electron goes down from an n
= 2 state to an n = 1 state of an atom a Kα characteristic x ray is emitted.
ABSORPTION COEFFICIENT - The physical parameter that characterizes the
absorption of electromagnetic radiation (x rays) per unit length of absorber.
Typical values of absorption coefficients for x rays from ~10 -3 cm-1 for air to
1 cm-1 for water to ~103 cm- 1 for gold, platinum and lead.
ANSWERS TO QUESTIONS FOUND IN THE TEXT
SECTION 30.1 Introduction
The fact that x rays penetrate body tissue while being absorbed by bone and that
x rays will expose photographic emulsions enable us to use x rays to photograph the
interior portions of human beings.
Since x rays are photons of a few thousand electron volts and since the electrons
in color television sets are accelerated through electric potentials of several
thousands of volts, x rays will be produced whenever the high energy electrons
strike suitable targets.
The detection of x rays first occurred because they expose photographic
emulsions. Now more quantitative measurements of x-ray intensities are made
using ionization chambers and scintillation counters.
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EXAMPLES
X- RAY PROBLEMS
1. An x- ray tube is operated at a peak voltage of 250 kV and a current of 1.0mA.
Then the exposure rate is 2.5 R/hr at a distance of 1.5 m from the target. (a) What
is the minimum wavelength of x-ray radiation emitted from this tube? (b) If the
current is increased to 20.0 mA what is the exposure rate at 1.5 m from the target.
(c) At what distance for the increased current can the exposure be reduced back
to 2.5 R/hr.
What data are given?
Accelerating voltage = 250 kV = 2.5 x 105 V
Current = 1.0 mA = 1.0 x 10-3 A
Exposure = 2.5 R/hr at a distance of 1.5 m.
What data are implied?
We will assume an inverse square law relationship between exposure and
distance.
What physics principles are involved?
The conservation of energy as expressed in Equation 30.1 can be used. The
definitions of radiation units (Section 30.6) and the inverse square law will also
be used.
What equations are to be used?
λV = 1240 eV•nm
(30.2)
I ∝ (1/d2)
(16.12)
Solutions
(a)
λmin = 1240eV•nm / 2.5 x 105 V
λmin = 4.96 x 10-3 nm ≈ 5.0 x 10-12 m.
(b) If the current is increased to 20 mA then the power of the tube is increased by
a factor of 20, so the intensity of x-ray radiation from the tube is increased by
a factor of 20, so the exposure rate is increased by a factor of 20 to a value of
50 R/hr.
(c) In order to reduce the exposure rate back to 2.5 R/hr the distance from the
target must be increased
(Dose) (distance)2 = constant
(50 R/hr) (1.5m)2 = 2.5 R/hr (X2)
(SQR RT(20)) (1.5 m) = x
6.7 meters = x
Thinking about the answers
Remember dose rates increase linearly with the tube current. High current,
high voltage x-ray sources ought to be avoided. If you can keep a large distance
away from sources of radiation you can reduce your exposure.
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PRACTICE TEST
1. A target of copper will produce X-rays when bombarded with high speed
electrons. A typical graph showing the X-ray spectrum produced is shown
below.
a) What approximate electron energy (in eV's) is required to produce X-rays from a
target like copper?
b) What produces the Bremsstrahlung? What is the origin of the two "peaks" called
the characteristic X-ray spectral lines?
2. A technician operates an X-ray machine at 200 kV peak for therapeutic purposes.
a) Find the energy and wavelength of the most energetic x-rays emitted.
b) This machine operates at an exposure rate of 1.0 R/min at a distance of 1.0 meter
from the machine. The recommended dosage for the technician (for a 40 hour
week) is 1.0 x 10-4 R/min. How thick should the lead shield be for protecting the
technician? (Given: The density of lead (ρ) = 11.4 gram/cm3. The ratio (µ/ρ) for
lead at 200 KeV = 0.80 cm2/gm.)
3. The interactions of radiation with living matter depends upon many factors and
are therefore complex. In general, absorbed radiation produces changes in cells.
a) Rate the following as most sensitive (MS), sensitive (S) or less sensitive (LS) to the
effects of radiation.
____ bone marrow cells
____ lymphoid cells
____ bone cells
____ blood vessel cells
____ muscle cells
b) What properties of cells and their response to radiation allows the radiation
treatment of cancer to be effective?
ANSWERS:
1. 20- 50 KeV (The accelerating voltage must be approximately 20,000 to 50,000
volts.) The Bremsstrahlung is white noise or background radiation produced by
the deceleration of the electrons upon impact with the target. The "peaks" are
produced by the excited target atoms. This energy allows target electrons to
return to a ground state after excitement and produce similar radiation
frequencies.
2. a) 200 KeV, 6.2 x 10-12 m, b) 1.0 cm
3. MS, LS, LS, MS, LS. Radiation treatment has shown that cells which reproduce
rapidly are the most sensitive to obstruction. Thus rapid growing cancerous cells
can be selected for destruction with proper levels of radiation which can allow
healthy cells to survive.
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