From 1895 to 1905, physicists are confronted to all sorts of new discoveries in a short period of time:

1895 Roentgen discovers X-rays

1896 Becquerel discovers radioactivity
1897 Thompson identifies electrons
1900 Planck sets the fundamentals of quantum theory
1905 Einstein defines the principles of relativity

These discoveries, which are mainly focused on the atomic structure, are the basis of modern physics

I. OBJECTIVE OF THE EXPERIMENT

We shall study the production, properties, and interaction with matter of X-ray

II. BASIC THOERY

23
The electromagnetic radiation spectrum (Fig. 1) ranges from approximately 1 Hz to 10 Hz .
12
Electromagnetic radiation of frequency greater than 10 Hz comes from molecular or atomic processes.

Fig. 1: Electromagnetic spectrum

We can divide electromagnetic radiation of atomic origin into three different categories:
12 17
- Light (infrared, visible and ultraviolet) whose frequency can vary between 10 and 10 Hz , comes from
perturbations of the electrons on the outermost shells of an atom.
17 20
- X-rays have a frequency that ranges from 10 to 10 Hz approximately, and are emitted from
perturbations of electrons on the inner shells of an atom.
19 22
- Gamma radiation’s frequency range is approximately 10 - 10 Hz . In contrast to the previous two
types of radiation, these rays come from the nucleus of radioactive atoms.
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE H5-2
PROPERTIES OF X-RAYS
X-rays behave differently than light in a number of different ways: no reflection on mirrors, no refraction
through prisms or lenses and no diffraction through thin slits. They are transparent to most bodies, even
metals. These phenomena are due to the wavelength of X-rays, which is much shorter than visible light.

PRODUCING X-RAYS
filament
The easiest way to perturb the inner electron layers of an atom in
cathode
order to cause it to radiate X-rays is to bombard it with high
velocity electrons. These electrons have a high enough energy to canon à
go by the outer layers of the atom and perturb the inner ones. 40 kV électrons
In practice, this electron bombarding is achieved in a tube with a
high vacuum. The electrons are emitted from a heated filament
(cathode), and are accelerated by an electrode (grate) brought to anode
voltage of the order of 40 kV . These electrons then hit an Rx
e-
molybdenum anticathode that absorbs electrons and emits X-
rays (Fig. 2).
Other materials can be used for the anticathode as well, e.g.:
Cr, Fe, Co, Ni, Cu, W .
anticathode
Mo

Tube Rx
Fig. 2: Scheme of an X-ray tube.

Two types of radiation occur

The continuous spectrum (Fig. 3) is due to the sudden

braking of electrons that pass by a nucleus, without ionizing
the atom. Most of the energy is dissipated in the form of heat.
However, electrodynamics predict that braking electrons
must also emit electromagnetic radiation. The energy w
that the electron loses is used to emit a photon of energy h.
w can have any value below the kinetic energy of the
electron eV . Therefore, the emitted photon can have any
wavelength as long as it satisfies eV  hv 

The lower limit is given by the equation:

c ch 12400
min    (1)
vmax eV V Fig. 3: Continuous spectrum of X-rays
corresponding to different acceleration voltages

where h is the Planck constant,  the frequency of the radiation, e the elementary charge, V the
10
acceleration voltage in volts and  the wavelength in Angstroms ( 10 m ).
The discrete spectrum is generated when an electron loses its energy inside an atom, and tears away an
electron on an internal layer (K, L,...). In a very short amount of time, an electron from an outer layer
replaces the missing electron, and emits a photon in the X-ray range in the process. The frequency of the
photon is proportional to the energy difference between the two involved electron layers.
1
v12   E2  E1  (2)
h
The energy difference between two neighboring layers is greatest for the innermost two layers (Fig. 4).
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE H5-3

Fig. 4: Simplified energy diagram.

Fig. 5: Characteristic spectrum

Comments:

1) Since the Ei (i=K, L, M,...) are discrete, the corresponding spectrum will be discrete as well (line
spectrum). The notation used to represent a line is the following: a letter is used to describe the final
layer of the electron, and a greek letter subscript indicates the initial layer of the electron. If an electron
goes from L to K, we have a K line. If instead it starts from M, we have a K line.
2) Since the configuration of an atom’s electronic layers depends on the element, the discrete spectrum X
is a characteristic of the material used for the anticathode (Fig. 5).
3) The line spectra for X-rays tend to be much simpler than the optical spectra. They are made of a small
number of lines called K, L, M, …
4) Since the configuration of the internal layers is pretty similar for all elements, the X-ray line spectra are
rather similar, and depend of the atomic number Z. Mosely found a simple equation connecting the
frequency of a line  to its atomic number. The equation is:
v  C Z  B
2
(3)

where C B are constants characterizing an element.

EFFECT OF X-RAYS ON MATTER

When a beam of X-rays goes through a material, we can macroscopically observe a drop in the X-ray’s
intensity. This effect is mostly due to two processes: the Compton effect and the photoelectric effect.

The Compton effect occurs when an X-ray photon collides with a free electron. The X photon loses energy
in the collision, and the energy is recuperated by the electron in the form of kinetic energy (Fig. 6).

The photoelectric effect occurs when an X photon is absorbed by an electron tied to an atom, and thereby
frees it from the atom.

Electrons freed from an atom through the photoelectric or Compton effect constitute  radiation, which
define the physical, chemical and biological actions of X-rays. The Compton effect dominates high-energy X-
rays (hard radiation), whereas the photoelectric effect the more important one for lower energy rays (soft
radiation).
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE H5-4

Fig. 6: Dispersion of the Compton photon

Due to their absorption by matter, the intensity of an X-ray (energy per unit surface and time) decreases as a
function of thickness according to the following formula:

I  I 0e md (4)

where, m is the absorption coefficient, d the thickness of the material and I 0 the incident radiation. The m
coefficient depends mostly on the material and the frequency of the incident beam. We can observe
discontinuities of the absorption due to the photoelectric effect.

INTERACTION OF X-RAYS WITH ANISOTROPIC MATTER - DIFFRACTION

A diffraction phenomenon occurs when an

incident wave of frequency  hits a grating of
small slits (  ) with regular spacing
( g   ). The outgoing wave’s direction is g
modified according to the equation:

g sin   n  

where n is an integer (Fig. 7).
Fig. 7: Diffraction of parallel beams by a grating.

In 1912 von Laue managed to diffract X-rays by directing them through a zinc sulfate crystal. W.H. and W.L.
continued von Laue’s experiments and found the X-ray diffraction conditions in a crystal. They studied
families of parallel planes in a crystal lattice (fig. 8).

For two neighboring parallel planes p1 and p2

the reflected waves reinforce one another if the
optical length MK  KN (Fig. 8) is an integer
 
p


multiple of the wavelength  , i.e. if:
p M N
 K d
p
 2d sin   n (5)

This equation is called Bragg’s law.

Fig. 8: X-ray – parallel plane interactions in a crystal
lattice. These discoveries have become the basis of X-
ray spectroscopy, as well as the basis for
studying the structure of solids.

BIOLOGICAL EFFECTS

Biological effects of X-rays are due to chemical or structural modifications of the cell composition. These
modifications can be of two types: somatic and genetic.

Somatic effects are internal or external lesions, and sometimes even burns, leading to poor health, and
possibly death. Genetic effects affect the eventual descendants of the irradiated organism. Living tissues are
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE H5-5
damaged by X-rays, and it is therefore crucial to control the amount of energy received by the organism. This
is how we shall define radiation dosage.

The absorbed dose of radiation is the physical quantity that measures the amount of absorbed ionizing
radiation per unit mass of the material. The SI unit is gray, defined as 1 Gy = 1 J/kg. The corresponding cgs
unit is rad, defined as 1 rad = 0.01 Gy  102 J kg ".

III. EXPERIMENTAL SETUP

The apparatus producing the X-rays is mounted of a chassis that contains all necessary elements for
completing its task, including those for security purposes. The direct heating X-ray tube is directly supplied
by a self-rectifying high voltage transformer. The X-ray tube, the anti-radiation protection and the high
voltage transformer are all grouped in a grounded metallic box (Fig. 9).

Fig. 9 : X-Ray machine

Using the apparatus

All settings are done from the configuration panel.
X-rays are only emitted when the HV On/Off indicator is blinking. The button allows to activate and
deactivate the radiation.
To set the voltage or the current, press U or I respectively, and adjust the value using the wheel.
The t ,  and  limits are used to setup automatic scanning. t fixes the measuring time at each
position,.  sets the step between two measurements, and  limits lets you determine the minimal (↓)
and maximal (↑) angles of the automatic scanning.
To start the automatic scanning, hit coupled, and then scan on/off. Data is collected using the program
appareil à rayon X found on the computer.
The sensor, target, and coupled buttons allow you to manually change the angle of the sensor, the target, or
both simultaneously. The zero button sets all angle back to 0 °.

The “counter tube" (Geiger-Müller) is a cylinder containing a low pressure gas. A magnetic wire of small
diameter stretches along the axis of the tube. We then apply a voltage slightly lower than one that would
create a spontaneous discharge in the gas. When a fast particle enters the tube, it provokes an electric
EPFL-TRAVAUX PRATIQUES DE PHYSIQUE H5-6
discharge in the gas. In order to know how many particles go through the tube, we simply count the number
of electric pulses. This is how a Geiger counter works.

IV. EXPERIMENTS
1) a) Response of the Geiger-Müller tube as a function of the acceleration voltage and the emission current
of the electrons. (saturation domains?).
Line up the Geiger-Müller tube with the source. For acceleration voltages of 20 / 25 / 30 / 35 kV ,
measure the response R of the G-M tube as a function of current ( I  0  1 mA ).
Discuss the results. (Hint: paralyzable and unparalyzable dead time)

b) Detailed calibration for U  30 kV .

Suppose I  R where R is the response of the Geiger-Müller tube. Set U  30 kV , and measure the
response of the tube more precisely, for I  0  0.1 mA . Determine the range for which the response
is linear (verify for both high and low R values), and determine the slope p. Later on, we will approximate
R  p  I for values of I that are to big to be measured by the Geiger counter.

2) Measure of the X-ray diffractogram for different acceleration voltages (Bragg experience).
Using the automatic scan function, establish the diffractogram of a NaCl rock salt crystal. Scan with a
measuring time of 1s and a step of 0.1 ° from 2.5 ° to 25 °. Do these measurements for
U  20 / 25 / 30 / 35 kV .
Talk about the observed curves, and point out the different lines on the graph. Determine the
wavelengths of K et K  lines.
Determine the numerical value f the Planck constant h using min of the continuous spectrum (supposing
that we know the lattice constant of the used crystal).

3) Absorption versus width

We will use a cylinder with seven slits that are blocked by aluminum samples ranging in thickness from
0.5 to 3 mm. By placing the Geiger counter behind the slits, we can determine the absorption coefficient
for aluminum.
Verify the exponential relationship between the X-ray intensity and the sample thickness, and determine
the absorption coefficient of aluminum.

4) Absorption versus atomic number.

We will use a cylinder with 7 slits blocked by samples of plastic ( Z  6 ), Al ( Z  13 ), Fe ( Z  26 ), Cu
( Z  29 ), Zr ( Z  40 ), ( Z  47 ), all 0.5 mm thick.
Determine the absorption coefficient for each one of these materials, and discuss the relationship with the
atomic number.
For certain measurements, you will need to use the detailed calibration explicated in 1b).

5) Bragg experiment and X-ray diffractogram

Using a rotating apparatus, when the target rotates by an angle  , the counter rotates by 2 .
Calibrate the X-ray diffractogram using a known crystal (LiF or NaCl) (exp. 2).
Using this, determine the lattice parameter (distance between atomic planes) of an unknown crystal.
You can also use a zirconium filter in front of the X-ray source, in order to isolate the K line of
molybdenum.

6) Compton Effect (extra)

A first measure is done with an absorbent (copper sheet) placed in front of the diffuser (aluminum plate).
A second measure is done where the absorbent is placed behind the diffuser. The reduced measured
intensity in the second case with respect to the first, shows that the wavelength of the X-ray photon is
increased during the diffusion.