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Physics of the Atom
The Atom and its components
The atom consists of a central small, massive nucleus made of Z
positively charged protons and N charge neutral neutrons surrounded
by a cloud of Z very light, pointlike, negatively charged electrons.
Z protons(p+)
and N
neutrons(n0)
Z electrons(e-)
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Units of Length, Mass and Charge
Length
Atomic size unit -1 Angstrom = 1 Ǻ = 10-10 m
Nuclear size unit -1 femtometer = 1fm = 10-15m ~ rp, rn
Size of electron – pointlike ie zero size
Mass
The unit of mass is the ATOMIC MASS UNIT (u):
1u = 1.66054 10-27 kg
Mp~ 1.0073 u
Mn~ 1.0087 u
Me ~ 0.00055 u
Charge The charge of the proton = +1.6 10-19 Coulomb =+ e
The charge of the electron = -1.6 10-19 Coulomb = -e
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Electrons in the atom
So a typical atom has a tiny massive nucleus a few fm (10-15 m) radius
with an electric charge of + Ze from its Z positively charged protons
To make the atom electrically neutral, surrounding this nucleus at
distances up to several Ǻ ( 10-10 m) is a cloud of Z negatively charged
electrons, with a total charge of -82e.
Most of the atom is vacuum containing only light, pointlike electrons.
Apart from the mass of the atom it is the distribution and energies of
these that are primarily responsible for the classical chemical and
physical properties of the atom.
What happens when a negatively charged electron is near a positively
charged nucleus?
http://www.colorado.edu/physics/2000/applets/orbits.html
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Electron Shells
Comparing the atom to the solar system
– In the solar system the motion of a planet is governed primarily
by the gravitational force between the sun and the planet and
Classical Mechanics
- In the atom the motion of an electron is governed primarily by the
Coulomb force between the nucleus and the electron and Quantum
Mechanics
-Quantum Mechanics leads to electrons being distributed about
the nucleus in orbital ‘shells’ with certain Radii and Energies.
The unit of energy used is the electron-volt, the energy a charge of e
=1.6 10-19 Coulomb gains when accelerated through 1 volt.
1eV= 1.6 10-19 Joules.
How many electrons can be in each shell?
http://www.colorado.edu/physics/2000/applets/orbits.html
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How many electrons can be in each shell (continued)?
The shells are identified by a number
n = 1,2,3…. with the n=1 shell being closest to the nucleus
and a number
l , giving the Angular Momentum of an electron in the shell.
l has values 0,1,2,3,4 … up to the value (n-1)
There can be maximum of 2(2l+1) electrons within a shell
We still have 1920s symbols for angular momentum
0 = s, 1=p, 2=d, 3=f, 4=g, 5=h
With this rule we can build up a picture - the Periodic Table –of the
atoms of all the elements…..
http://www.colorado.edu/physics/2000/applets/a2.html
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X-Ray Spectra
In an X-ray tube we can bombard atoms with high energy electrons say with 10 keV energy.
Electrons
H.T.
V kV
-
X-ray detector
+
X-rays
Anode
A 10 keV electron may knock out an electron from an inner shell –
leaving a vacancy in the shell. An electron in a higher shell will then
drop down, losing energy, to fill the vacancy. This energy it loses is
emitted as light. http://www.colorado.edu/physics/2000/index.pl. 6
What are X-rays?
We call this light, resulting from knocking out an inner shell electron,
X-radiation or X-rays
Light wave, velocity c m/sec, wavelength  m, frequency  sec-1
c m/sec
m
(a)
Frequency is the number of wavelengths that pass a point - say point (a) per sec.
= c / 
Associated with frequency is energy: E = h  keV
where h is Planck’s constant :
h = 4.136 10-18 keV sec
E = I(inner shell) – I(outer shell)
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A typical X-ray spectrum from a tungsten anode. The lines are
characteristic of tungsten atoms, the continuum arises from
bremsstrahlung (braking radiation) as the incident 10 keV electrons are
decelerated by interactions with the tungsten nuclear electric field.
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Understanding the X-ray spectrum
We divide the X-ray spectrum into a continuum background plus a line
spectrum.
Why does the continuum have a short wavelength cut-off point?
The continuum has a short wavelength cut-off point corresponding to the
incident electron losing all its energy in the anode material.
Eelectron= eV = hmax = hc/min
i.e. min = hc/eV
This, in fact, provides a very accurate method of measuring h - Planck’s
constant.
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Line spectrum
This is due to a bombarding electron knocking out an inner shell
electron from an atom of the anode. Electrons in higher shells then drop
down sequentially to fill first the hole created in that shell, then the
subsequent holes created in higher shells.
Example
Let the electron in an anode atom that the bombarding electron knocks
out be in the n=1 shell.
Then electrons in higher shells can de-excite :
n=2  n=1.
n=3  n=2 or n=1
n=4  n=3 or n=2 or n=1
Hence we get the X-ray line spectrum.
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Moseley’s Laws
Moseley observed a regularity in line spectra from different anode
elements.
Using spectroscopic notation:
n
1
2
3
4
5….
K
L
M
N
O…..
Moseley obtained data for two prominent lines known as the K, L lines
for different anode elements.
K L  K transition
L M  L transition
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He noticed that the wavelengths of these line could be fit by simple
formulas ( Moseley’s Laws):
For K
1/ ~ C K (Z-1)2
For L
1/ ~ C L (Z-7.4)2
Now quantum mechanics predicts the energy of a shell to be:
En = -(13.6/n2)Z2 eV
Therefore the energy of X-rays emitted when an electron drops from a
level with n=n1 to a level with n=n2 is:
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E 12 = hc/  = 13.6 (1/n22 -1/n12) Z2
Thus, dividing by hc:
For the K line: 1/ = [13.6 (1/12 – 1/22)/hc] Z2 = C K (Z-1)2
For the L line: 1/ = [13.6 (1/22 - 1/3 2)]/hc] Z2 = C L (Z-7.4)2
In both cases the square bracketed quantities gave good agreement with
C K and C L . The factors (Z-1)2 and (Z-7.4)2 rather than Z2 were
explained as being due to the ‘screening effect’ of electrons between the
nucleus and the electron interacting with the bombarding electron.
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Auger Electron Emission
An alternative to X-ray emission as the atom de-excites is the emission
of Auger electrons:
Knocked out electron
Incident
electron
Auger
Electron
K
L
If a hole has been created by electron bombardment in the K-shell,
then an L shell electron may de-excite to the K-shell, losing energy
NOT by emitting an X-ray but by giving its excess energy to
another electron in the L-shell.This is then emitted as the Auger14
electron.
The kinetic energy of the Auger electron,
TAuger = (IK - IL) - IL
where IK, IL are the energies required to remove an electron from
an energy level.
Fluorescent Yield
This is a measure of the probability of X-ray emission rather than
Auger emission for different elements. It is the number of X-rays
emitted per vacancy in a given shell. For instance if there is a
vacancy in the K-shell - created by electron bombardment say then the fluorescent yield is K.
K = KL + KM + KN ...
the sum of X-rays emitted from higher shells per vacancy in the15
K-shell.
1
K
0
20
40
60
80
Z
So light atoms, when excited by external bombardment, decay
preferentially by Auger electron emission, heavy elements decay by X-
ray emission.
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