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Bohr’s model of H atom

Bohr’s model of H atom. PHY123. Niels Bohr (1885-1962). By Iutta Waloschek. Hydrogen atom. Positively charged nucleus inside ( +Ze ), negatively charged electron ( -e ) around Electron is attracted to nucleus Electron is trapped in a potential well created by nucleus (“a box”)

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Bohr’s model of H atom

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  1. Bohr’s model of H atom PHY123 Lecture XIII

  2. Niels Bohr (1885-1962) Lecture XIII By Iutta Waloschek

  3. Hydrogen atom • Positively charged nucleus inside (+Ze), negatively charged electron (-e) around • Electron is attracted to nucleus • Electron is trapped in a potential well created by nucleus (“a box”) • Energy levels in atom Lecture XIII

  4. Standing electron waves in Hydrogen atom • Standing waves: • 2prn=nl l=h/mv mvrn=nh/2p • Angular momentum L=mvrn is quantized L=nh/2p • n – orbital quantum number Lecture XIII

  5. Disclaimer • Though Bohr’s model was able to predict many properties of H atom and correctly calculate some of its characteristics, this model is incomplete and it is not advisable to think of an atom as a miniature “solar system”. • Orbits make sense only as average radii of electron position (not the same as electron slightly smeared around circular orbits!!!) Lecture XIII

  6. Hydrogen atom • mvrn=nh/2p v=nh/(2pmrn) • Newton’s 2nd law for circular motion: Bohr radius Lecture XIII

  7. Hydrogen atom • Energy in H atom KE+U Lecture XIII

  8. Hydrogen atom • What did we learn? • For high n energy approaches -0, radius approaches infinity • Energy proportional to Z2e4 • Ze2 from the potential, Ze2from 1/r (smaller orbits around larger charges) • Radius inversely proportional to mass (F=mv2/r)  Energy proportional to electron mass • Energy does not depend on nucleus mass – assume infinitely heavy • In classical case (h0) rn0 – electron falls on nucleus. Lecture XIII

  9. Hydrogen atom • Energy levels in H • Infinite number of states n=1-infinity • All energies are negative – electron is trapped in atom • Lowest possible energy level E1=-13.6 eV – ground state • Positive energy – free electron –ionization • Ionization energy =13.6/n2for atom in n state Lecture XIII

  10. Some parameters of the H atom • Ground state n=1, Z=1 • Electron’s “orbit” radius • Wavelength • Momentum • v/c Lecture XIII

  11. Some parameters of the H atom • Ground state n=1, Z=1 • Kinetic Energy • Potential Energy • Total energy • Longest wavelength absorbed (l – max E =hc/l – min) n=1n=2 E1=-13.6eV E2=-13.6/4=-3.4eV Eg=13.6-3.4=10.2eV l=hc/Eg=1243eVnm/10.2eV=122nm Lecture XIII

  12. A cute problem • Electrons are accelerated by 12.3V potential difference and pass through hydrogen gas at room T (ground state n=1). Which wavelengths of light can be observed? Lecture XIII

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