Ch6 X-ray
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Producing X-ray
Moseley formula
X-ray diffraction
Compton effect
Absorption of x-rays
Some Words
• X-ray
• Moseley’s model
• Moseley's empirical
formula
• electromagnetic
spectrum
• Bremsstrahlung (轫致
辐射)
• Characteristic x-ray
• Bombard (轰击)
• Graphite (石墨)
• Vacancy
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Molybdenum (钼)
Compton scattering
Interaction
Absorption coefficient
Absorption edge
Positron (正电子)
Photoionization
Pair formation
Attenuate (衰减)
Binding energy
X-rays
• X-rays mean electromagnetic radiation which
has a wavelength shorter than that of ultraviolet
light. 0.003-1nm, 1-500keV, or 1-100keV
• X-rays can be produced when electrons,
accelerated through a large potential difference,
collide with a metal target.
• A plot of x-ray intensity per unit wavelength
versus the wavelength consists of sharp peaks or
lines superimposed on a broad continuous
spectrum (Bremsstrahlung).
• The cut-off frequency of the Bremsstrahlung is
determined by the KE of the impinging electrons.
X-ray spectrum
• X-ray is produced
when a molybdenum
target is bombarded
with electrons of
35keV.
• It includes
Bremsstrahlung
continuium &
characteristic lines.
hc
1.24
• There is cut-off
 

nm
1eV V (kV )
frequency.
min
Brehmsstrahlung
• "Bremsstrahlung" meaning "braking
radiation" describes the radiation which is
emitted when electrons are decelerated or
"braked" when they are fired at a metal target.
• Accelerated charges give off electromagnetic
radiation, and when the energy of the
bombarding electrons is high enough, that
radiation is in the x-ray region of the
electromagnetic spectrum.
• It is characterized by a continuous
distribution of radiation which becomes more
intense and shifts toward lower wavelength
when the energy of the bombarding electrons
is increased.
Characteristic x rays
• There must be a vacancy in a subshell of an atom
to produce characteristic x-rays.
• The bombarding electrons can eject electrons
from the inner shells of the atoms of the metal
target.
• Those vacancies will be quickly filled by
electrons dropping down from higher levels,
emitting x-rays with sharply defined frequencies
associated with the difference between the
atomic energy levels of the target atoms, called
characteristic x-rays.
K, L, M series in x-ray
• K lines involve K shell of a
metal atom.
K (n  2  n  1), K  (n  3  n  1),
– K shell electron is knocked
out of the atom.
– An electron in a outer shell
falls into the K shell.
K (n  2  n  1), K  (n  3  n  1),
• L lines involve L shell of a
metal atom.
– L shell electron is knocked
out of the atom.
– An electron in a outer shell
falls into the L shell.
L (n  3  n  2), L (n  4  n  2),
Moseley plot
• When the square
root of the
frequencies of the
characteristic xrays from the
elements is plotted
against the atomic
number, a straight
line is obtained.
Moseley’s formula
• Moseley showed that the characteristic x-rays
followed a straight line when the atomic
number Z versus the square root of frequency
was plotted.
• With the insights gained from the Bohr model,
we can write his empirical (经验的)
relationship as follows:
  A( z   ) 2
~K  R 34 ( Z  1) 2 ~L  R 365 ( Z  7.4) 2
X-ray diffraction
• Like electron diffraction, x-rays can be diffracted
by a crystal.
• When x-rays are incident on a crystal in which
atoms are arranged in regular array and act as an
optical grating, the scattered waves will interfere in
some directions.
• The atoms in a crystal may be thought of as
families of parallel planes known as Bragg planes.
• The Bragg equation for maxima in the diffraction
pattern is:
n  2d sin 
Compton effect
• Compton effect, Compton
(1892-1962) showed that
monochromatic X rays are
scattered by graphite (石墨),
and their wavelength increases
by:
• The collision between a
photon and an electron is
regarded as an elastic collision.
• Compton wavelength of
electron:
 

h
(1  cos  )
m0 c
2h

sin 2
m0 c
2
h  m0c 2  h '  mc2
 '

p  p  mv

hc
 0.00243nm
2
m0 c
Compton scattering
• Compton first to measure
photon-electron scattering
in 1922.
• When the incoming
photon gives part of its
energy to the electron,
then the scattered photon
has lower energy.
• The wavelength change in
such scattering depends
only upon the angle of
scattering for a given
target particle.
Photon interaction with matter
• There are three ways:
– Photoionization, giving all of the energy to an
electron.
– Compton scattering: giving part of the energy
to the electron and the remainder to a lower
energy photon.
– Pair production: At sufficiently high energies
(>1.02MeV), the photon can create an
electron positron pair.
• Generally, x-ray’s interaction is mainly in first
two ways.
X-ray absorption
• X-rays, like other electromagnetic radiation, are
absorbed and scattered on passing through matter.
• The transmitted intensity is given by:
 x
  x
I  I 0e intensity,
 I 0e
– I0: incident
– μ: absorption (Photoionization absorption + scattering) or
attenuation coefficient,
mass absorption

coefficient,
– x: the thickness of the material irradiated,
• µ depends strongly on x-ray energy E and atomic
number Z, and on the density ρand atomic mass
A.
Absorption
Absorption edge
Photon Energy
• If the wavelength of the X-rays is
reduced so that their energy is equal
to one of the energies of the atomic
levels of the absorber, a sudden
increase in absorption is observed.
• It corresponds to the photon energy to
knock out an inner electron.
• In X-ray spectrum, the K-absorption
edge for each element is slightly less
than that for the K-emission spectrum.
• This feature of x-ray absorption edge
has some applications, such as filter,
spectrum differentiation & coronary
angioplasty.
Example1
• Question: The K absorption edge wavelength
for uranium (Z=92) is 0.107Å and its Kα line is
0.126Å. Find the wavelength of its L
absorption edge.
• Answer:
EK 
hc
K
n=inf
 119.5keV ()
EL  EK 
hc
 K
 98.4keV
E L  17.5keV ()
L 
BE L  hcL
hc
 0.0709nm
 EL
BE K 
L
Kα
K
hc
K
Example 2
• Question: A beam of electrons with 100keV are
bombarding the target. The binding energies for the inner
shells for the target atom are listed in the table. Find the
possible x-rays and their wavelength.
shell
K
LI
LII
LIII
MI
MII
MIII
MIV
MV
electron
1s
2s
2p
2p
3s
3p
3p
3d
3d
2.520
0.505
0.410
0.393
0.230
0.227
BE (keV) 20.00 2.866 2.625
• Solution: Determine the energy level of subshells from
the binding energy. Using selection rule to determine the
possible transitions and then calculate the wavelengths.
– Total: 12 lines: K-alpha (2), K-beta (2), L-alpha (7)
The transitions
M
shell
V
IV
Ⅲ
Ⅱ
Ⅰ
1 2
L
shell
1 2 3 4 5 6 7
Ⅲ
Ⅱ
Ⅰ
Lα
3d
3d
3p
3p
3s
2D
5/2
2D
3/2
2P
3/2
2P
1/2
2S
1/2
2p
2p
2s
2P
3/2
2P
1/2
2S
1/2
1s
2S
1/2
8
1 2
K
shell
Kα
Kβ