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

lasers