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Download Astr 250 Notes on the Bohr Model Classical model
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Astr 250 Notes on the Bohr Model Classical model - centripetal force provided by the Coulomb attractive force to keep an electron in a circular orbit about a nucleus (see figure below) - problem is that electron radiate when accelerated, thus should be losing energy in circular orbits, thus atoms would be collapsing. Bohr model - assumed only certain orbits are allowed, and those do not radiate. - that these allowed orbits have discrete angular momentum, L = n h / 2π . - replaces particles with standing waves (wavefunctions), where n is number of waves in the orbit (see figure below). Equations in the Bohr model Angular Momentum: L = n h /2π = m v r Centripetal Force: Fcp = mv2 / r = k Z e (e / r2) Total Energy: E = ½ mv2 - k Z e2 / r These three equations can be used to find the orbital radii and energy level per principle quantum number (n) r(n) = n2 [ h2 / 4π2 m e2 k Z] E(n) = - [ 2π2 m e4 k2 Z2 / h2 ] / n2 For the ground state of hydrogen, n = 1; r(n=1) = 0.0529 nm = ao (the Bohr radius) E(n=1) = -13.6 eV ΔE = E(m) – E(n) = hc / λ where this is the wavelength of light emitted when the electron transitions between energy levels, and not the wavefunction of the orbit of the electron (see above).