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The Bohr model - charge of-e while the nucleus has a charge...

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The Bohr model The Bohr model is a planetary model of the atom that explains things like line spectra. Neils Bohr proposed that the electrons orbiting the atom could only occupy certain orbits, orbits in which the angular momentum satisfied a particular equation: where m is the mass of the electron, r is the radius of the orbit, and v is the orbital speed of the electron. In other words, Bohr was proposing that the angular momentum of an electron in an atom is quantized. What does quantization of the angular momentum mean for the energy of the electron in a particular orbit? We can analyze the energy very simply using concepts of circular motion and the potential energy associated with two charges. The electron has a
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Unformatted text preview: charge of -e, while the nucleus has a charge of +Ze, where Z is the atomic number of the element. The energy is then given by: The electron is experiencing uniform circular motion, with the only force on it being the attractive force between the negative electron and the positive nucleus. Thus: Plugging this back into the energy equation gives: If you rearrange the angular momentum equation to solve for the velocity, and then plug that back into the equation: and solve that for r, you get: This can now be substituted into the energy equation, giving the total energy of the nth level:...
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