Derivation of the Rydberg Constant

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Derivation of the Rydberg Constant

• An introduction to the Bohr Model of the Atom

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Empirical formula discovered by Balmer to
describe the hydrogen spectra
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Lyman, Paschen, BrackettPfund Series
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Energy of a photon
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Bohr Model
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Energy of an atom
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Newtonian mechanics
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Fnet equals Coulombic attraction
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Convenient expression
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Energy of an atom
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After simplification
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Recall rotational mechanics
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Bohr Postulate

• Electrons in a stable orbit do not radiate. That
  is, atoms are stable and do not collapse.
• Electrons in transition from a higher to a lower
  energy state radiate a photon of energy hf.

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Bohr Postulate
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Angular Momentum
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Combining expressions
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General formula for the radius
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Bohr radius
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Energy levels of the atom
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Bohr Energy Levels
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Energy of a photon
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Rydberg Constant!
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Limitations of the Bohr Model

• Works well for hydrogen, and for other single
  electron atoms, but not as well for helium and
  even less well for other atoms
• Based upon postulates that angular momentum is
  quantized