Quantum Theory of the Atom

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Presentation of Lecture Outlines, 7–15

(6.626 x 10-34 J.s) x (1.255 x 106 s-1) =

8.3156 x 10-28 = 8.316 x 10-28 J

Solve for E, using E = hn, and four

significant figures for h.

What is the energy of a photon corresponding to radio waves of frequency 1.255 x 10 6 s-1?

Slide 16

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Presentation of Lecture Outlines, 7–16

The Bohr Theory of the Hydrogen Atom

Prior to the work of Niels Bohr, the stability of the atom could not be explained using the then-current theories.

In 1913, using the work of Einstein and Planck, he applied a new theory to the simplest atom, hydrogen.

Before looking at Bohr’s theory, we must first examine the “line spectra” of atoms.

1913—Nobel Prize in 1922

Slide 17

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Presentation of Lecture Outlines, 7–17

Bohr’s Postulates

Bohr set down postulates to account for (1) the stability of the hydrogen atom and (2) the line spectrum of the atom.

1. Energy level postulate An electron can have only specific energy levels in an atom.

2. Transitions between energy levels An electron in an atom can change energy levels by undergoing a “transition” from one energy level to another.

The Bohr Theory of the Hydrogen Atom

Slide 18

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Presentation of Lecture Outlines, 7–18

Bohr’s Postulates

Bohr derived the following formula for the energy levels of the electron in the hydrogen atom.

Rh is a constant (expressed in energy units) with a value of 2.18 x 10-18 J.

The Bohr Theory of the Hydrogen Atom

Slide 19

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Presentation of Lecture Outlines, 7–19

Bohr’s Postulates

When an electron undergoes a transition from a higher energy level to a lower one, the energy is emitted as a photon.

The Bohr Theory of the Hydrogen Atom

Slide 20

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Presentation of Lecture Outlines, 7–20

Bohr’s Postulates

If we make a substitution into the previous equation that states the energy of the emitted photon, hn, equals Ei - Ef,

Rearranging, we obtain

The Bohr Theory of the Hydrogen Atom

Slide 21

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Presentation of Lecture Outlines, 7–21