LECTURE 04 Quantized atom

LECTURE 04 Quantized atom - SUMMARY FROM LAST CLASS...

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Dr. P. Lucas U of A MSE 110 Quantization SUMMARY FROM LAST CLASS 1885: Balmer analyzed the emission spectra of atoms in gas discharge tube and showed that wavelength of the emitted lines followed the empirical relation: 1913: Bohr proposed a model for the hydrogen atom which rationalized Balmer’s observation. The electron can rotate around the proton on a series of specific orbits of radius r n and energy E n . The electron emits a photon h ν =E i -E f when it relaxes from a higher to a lower energy level. This correspond to the Balmer lines. Bohr’s model is based on the assumption that the angular momentum mvr of the electron is quantized (can only take certain values). As a consequence, r n and E n are also quantized. Their allowed values are defined by the quantum number n according to: Where Z is the charge of the nucleus (Z=1 for hydrogen) = 2 2 1 2 1 1 n R H λ m Z n a r o n 2 = eV n Z E n 2 2 6 . 13 =
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Dr. P. Lucas U of A MSE 110 Hence the electron orbit can only adopt a certain number of value proportional to the wavelength (n λ ). The orbits must satisfy n λ = 2 π r. This is the basis for the quantization of the radius and in turn the energy of the electrons revolving around the nucleus. De Broglie’s principle applied to atoms QUANTIZED ATOM Bohr’s model was very powerful to describe atoms and rationalize atomic spectra however it is based on the postulate (assumption) that the angular momentum mvr is quantized. Bohr just assumed it without real justification. The justification came from de Broglie principle that electrons behave as wave.
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This note was uploaded on 10/06/2009 for the course MSE 110 taught by Professor Lucas during the Spring '08 term at University of Arizona- Tucson.

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LECTURE 04 Quantized atom - SUMMARY FROM LAST CLASS...

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