Derivation of the Rydberg Constant - PowerPoint PPT Presentation

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Derivation of the Rydberg Constant

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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 ... – PowerPoint PPT presentation

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Title: Derivation of the Rydberg Constant


1
Derivation of the Rydberg Constant
  • An introduction to the Bohr Model of the Atom

2
Empirical formula discovered by Balmer to
describe the hydrogen spectra
3
Lyman, Paschen, BrackettPfund Series
4
Energy of a photon
5
Bohr Model
6
Energy of an atom
7
Newtonian mechanics
8
Fnet equals Coulombic attraction
9
Convenient expression
10
Energy of an atom
11
After simplification
12
Recall rotational mechanics
13
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.

14
Bohr Postulate
15
Angular Momentum
16
Combining expressions
17
General formula for the radius
18
Bohr radius
19
Energy levels of the atom
20
Bohr Energy Levels
21
Energy of a photon
22
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23
Rydberg Constant!
24
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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