Download Properties of Light

Atomic Structure
X-ray Spectrum
Characteristic
spectrum
Continuous spectrum
Atomic Structure
• Atoms have electrons in energy levels of increasing energy
• outer electrons are removed more easily than the inner electrons
• consider an electron of kinetic energy K passing close to an atom
• a “collision” in which the electron loses kinetic energy which appears as the
energy hf of a photon which radiates away from the atom
• x-rays are emitted ( bremsstrahlung)
• there is a minimum wavelength. Why?
X-ray spectrum
• If electron loses all its energy, eVaccel= hfmax = hc/min
• min is independent of the material and depends only on KE of electrons
• note that if h=0, then min =hc/eVaccel would be zero!
• the peaks at larger  depend on the material
• arise when the incident electron knocks out an inner electron
• this leaves a hole in an inner shell which is filled by an outer electron with
the emission of an x-ray photon
Note K K lines
K shell => n=1
L shell => n=2
M shell => n=3
Moseley Plot
• Moseley (1913) measured characteristic x-rays of as many
elements as he could find at the time
• he found that he could order the elements by atomic number Z
rather than by atomic weight (i.e. increasing number of electrons)
• for the K he plotted the square root of frequency vs position in
periodic table and found a straight line
• data could be fit to
f  C (Z 1)
f  C (Z 1)
Bohr Theory
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Characteristic x-ray spectrum identifies elements
depends on Z which determines the chemical properties
K-shell electrons are close to nucleus
visible spectrum involves transitions of outer electrons
Bohr theory works for hydrogen but not multi-electron atoms
however it works well for the Moseley plot
consider an L-electron (n=2 level) about to make a transition to
the K-shell which now only has one electron left
• L electron “sees” a net charge of Ze + (-e) = (Z-1)e
• more precise calculations find (Z-b)e where b~1
• Bohr theory for a transition E between n=2 and n=1 levels
E
1  3 2
2 1
f 
 13.6eV Z  2  2   Z (13.6) eV
h
1 2  4
Bohr Theory
• Replace Z by (Z-b) ~ (Z-1)
E
1  3
2 1
f 
 13.6eV ( Z  1)  2  2   ( Z  1) 2 (13.6) eV
h
1 2  4
3
f 
(13.6) eV (Z  1)
4
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Agrees fairly well with the experimental data for K-lines
does not work well for L-lines
need quantum mechanical treatment
does not work well at higher values of Z
Properties of Light
• Sunlight is composed of many wavelengths
Continuous visible
spectrum
Line spectra from
H, He, Ba, Hg
Photon-Atom Interactions
Energy of photon too small f `=f
Scattered photon has f ` < f
hf just matches E
Atom excited to higher level
and makes several transitions
Electron escapes and photon
absorbed
Photon-Atom Interactions
Much higher energy and
a photon is emitted
Atom in excited state
and hf matches E
Outgoing photon is in phase with incident photon and in same
direction => more photons!
Light from different atoms is coherent
Incoherent and
not monochromatic
Incoherent and monochromatic
Coherent and monochromatic
Lasers
• Light amplification by stimulated emission
of radiation
• produces a beam of coherent photons by
stimulated emission
laser
Ruby Laser
Normally all atoms are in the ground state E1
For the laser to work, we need more atoms in an excited state
--> called population inversion
Optical pumping is used to excite electrons to higher levels
which then relax to the state E2
Particle picture
Wave picture
lasers