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##### Atomic Structure

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**Characteristic**spectrum Continuous spectrum X-ray 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**M shell => n=3**L shell => n=2 K shell => n=1**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 Khe plotted the square root of frequency vs position in periodic table and found a straight line • data could be fit to**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**Bohr Theory**• Replace Z by (Z-b) ~ (Z-1) • 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