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Energy level diagrams and the hydrogen atom

Energy level diagrams and the hydrogen atom - and quantized...

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Energy level diagrams and the hydrogen atom It's often helpful to draw a diagram showing the energy levels for the particular element you're interested in. The diagram for hydrogen is shown on page 918 in the text. Hydrogen's easy to deal with because there's only one electron to worry about. The n = 1 state is known as the ground state, while higher n states are known as excited states. If the electron in the atom makes a transition from a particular state to a lower state, it is losing energy. To conserve energy, a photon with an energy equal to the energy difference between the states will be emitted by the atom. In the hydrogen atom, with Z = 1, the energy of the emitted photon can be found using: Atoms can also absorb photons. If a photon with an energy equal to the energy difference between two levels is incident on an atom, the photon can be absorbed, raising the electron up to the higher level. Angular momentum Bohr's model of the atom was based on the idea the angular momentum is quantized,
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Unformatted text preview: and quantized in a particular way. de Broglie came up with an explanation for why the angular momentum might be quantized in this way. de Broglie realized that if you use the wavelength associated with the electron, and only allow for standing waves to exist in any orbit (in other words, the circumference of the orbit has to be an integral number of wavelengths), then you arrive at the same relationship for the angular momentum that Bohr got. The derivation works like this, starting from the idea that the circumference of the circular orbit must be an integral number of wavelengths: Taking the wavelength to be the de Broglie wavelength, this becomes: The momentum, p, is simply mv as long as we're talking about non-relativistic speeds, so this becomes: Rearranging this a little, and recognizing that the angular momentum for a point mass is simply L = mvr, gives the Bohr relationship:...
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