atomic structure. x-ray spectrum continuous spectrum characteristic spectrum
Post on 22-Dec-2015
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Atomic Structure
X-ray Spectrum
Continuous spectrum
Characteristicspectrum
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
( 1)f C Z
( 1)f C Z
Bohr Theory• 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
2 22 21 1 3
13.6 (13.6)1 2 4
EeV e
hf Z Z V
Bohr Theory
• Replace Z by (Z-b) ~ (Z-1)
2 22 21 1 3
13.6 (13.6)1 2
1) (4
( 1)E
eV Vh
f Z Z e
3(13.6 ( 1))
4eVf Z
• 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 visiblespectrum
Line spectra fromH, 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 leveland makes several transitions
Electron escapes and photonabsorbed
Photon-Atom Interactions
Much higher energy anda photon is emitted
Atom in excited stateand hf matches E
Outgoing photon is in phase with incident photon and in samedirection => 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
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
Ruby Laser
Optical pumping is used to excite electrons to higher levelswhich then relax to the state E2
Particle picture
Wave picture