Quantum Theory of the Atom

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Each main “shell” is subdivided into “sub shells.” Within each shell of quantum number n, there are n sub shells, each with a distinctive shape.

l can have any integer value from 0 to (n - 1)

The different subshells are denoted by letters.

Letter s p d f g …

l 0 1 2 3 4 ….

Quantum Numbers and Atomic Orbitals

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Presentation of Lecture Outlines, 7–41

The magnetic quantum number (ml) distinguishes orbitals within a given sub-shell that have different shapes and orientations in space. Each sub shell is subdivided into “orbitals,” each capable of holding a pair of electrons. ml can have any integer value from -l to +l. Each orbital within a given sub shell has the same energy.

Quantum Numbers and Atomic Orbitals

The spin quantum number (ms) refers to the two possible spin orientations of the electrons residing within a given orbital. Each orbital can hold only two electrons whose spins must oppose one another. The possible values of ms are +1/2 and –1/2.

Slide 42

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Presentation of Lecture Outlines, 7–42

Why the different shapes?

1s

3s

2s

2px

3pz

3d

2py

2pz

3py

3px

s-shape

p-shape

d-shape

d-shape

Animations

Pictures

s-shape

p-shape

d-shape

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Presentation of Lecture Outlines, 7–43

Scanning Tunneling Microscope Electron Clouds

Image Movie

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Presentation of Lecture Outlines, 7–44

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Presentation of Lecture Outlines, 7–45

Figure 7.23: Orbital energies of the hydrogen atom. (Click here for non-hydrogen atoms)

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Presentation of Lecture Outlines, 7–46

Figure 7.24: Cross-sectional representations of the probability distributions of S orbitals.

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Presentation of Lecture Outlines, 7–47

Figure 7.25: Cutaway diagrams showing the spherical shape of S orbitals.

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