Derivation of the Rydberg Constant

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Presentation transcript:

Derivation of the Rydberg Constant An introduction to the Bohr Model of the Atom

Empirical formula discovered by Balmer to describe the hydrogen spectra

Lyman, Paschen, Brackett Pfund Series

Energy of a photon

Bohr Model

Energy of an atom

Newtonian mechanics

Fnet equals Coulombic attraction

Convenient expression

Energy of an atom

After simplification

Recall rotational mechanics

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.

Bohr Postulate

Angular Momentum

Combining expressions

General formula for the radius

Bohr radius

Energy levels of the atom

Bohr Energy Levels

Energy of a photon

Rydberg Constant!

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

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