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Unformatted text preview: The Bohr Model of the Atom Only orbits of specific radii and energies are allowed. r 1 = a energy levels get closer together as the electron moves to higher orbits i.e. the Bohr radius is effectively the radius of the hydrogen atom ( the first estimate for the size of atoms!!! ) R E 1 n 2 E n = r n = n 2 a The Bohr Model of the Atom Bohr solved this problem for the hydrogen atom by making the following assumptions: (1) The electron moves in circular orbits about the nucleus with motion described by classical physics. (2) Only a fixed set of orbits are allowed and in these orbits no energy is emitted . Allowed orbits are those in which the angular momentum (m e vr) is quantized in units of (nh/2 ), where n is the principal quantum number . (3) Electrons can only pass from one orbit to another and this is accompanied by discrete changes in energy. m e vr = n(h/2 ) = nh h = h/2 angular momentum The Bohr Model of the Atom Using these assumptions, Bohr demonstrated that the electron could circulate the atom in orbits of certain specific radii and with specific energies . R E 1 n 2 n = 1, 2, 3,... a 0 = Bohr radius = 0.529 R E = Rydberg energy = 2.18 x 10 18 J r n = n 2 h 2 e 2 m e = n 2 a 8 h 2 e 4 m e E n = 1 n 2 = The Bohr Model of the Atom E 1 E 2 Photon emitted + h Photon absorbed h E 2 E 1 Light is emitted when an electron jumps from a higher orbit to a lower orbit and absorbed when it jumps from a lower to higher orbit. The energy and frequency of light emitted or absorbed is given by the difference between the two orbit energies. E(photon) = h = E 2  E 1 The Resonance Condition Energy can only be absorbed or emitted if the frequency of the light corresponds exactly to the difference in energy of the initial and final states. E 1 E 2 + h h E 2 E 1 OK OK NO! NO! NO! NO! Absorption Emission E(photon) = h = E 2  E 1 Atomic Spectra As techniques advanced, more lines were discovered in the nonvisible regions of the atomic spectra of hydrogen. Rydberg noticed that all the lines could be predicted by the expression: = R H 1 n 1 2 1 n 2 2 n 1 = 1, 2,... n 2 = n 1 + 1, n 1 + 2,.. R H = Rydberg constant 1 Shortcomings of the Bohr Atom The Bohr atom was very important because it introduced the idea of quantized energy states for electrons in atoms....
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This note was uploaded on 11/03/2011 for the course MATH 1090 taught by Professor Greenwood during the Spring '08 term at MIT.
 Spring '08
 greenwood
 Calculus

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