Lecture 5 Atomic Theory 2

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Lecture 5 - Atomic Theory 2
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Review

• small, massive nucleus
• electrons occupy most of the volume
• white light ? all wavelengths
• atomic light source ? discreet wavelengths
• Plancks equation E hn

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Bohrs Atomic Model
Light Emission

Electron Excitation
n1
n2
n3
4
n¼
n5
n4
Paschen Series
n3
(IR)
Balmer Series (VIS)
n2
Lyman Series (UV)
n1
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Balmer-Rydberg Equation
Relates l to upper and lower transition levels
1
1
1
-
R
l
n2
m2
Upper level
Lower Level
R 0.01097 nm-1
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According to de Broglie,

• moving particles exhibit wave-like properties
• l h/(mv)

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by the way,

• Energy Force x Distance
• ma x d
• kg x (m s-2) x m
• kg m2 s -2
• J

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de Broglie Example

• An electron is moving at 2.74 x 106 m/s
• Find its wavelength!
• l h/(mv)
• 6.63 x 10-34 J s / (9.11 x 10-31 kg x 2.74 x
  106 m/s)
• 2.65 x 10-10 m 0.265 nm

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Enter Erwin Schrodinger

• forget the particles - atoms themselves are like
  waves
• Schrodinger wave equation

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Schrodinger wave equation

• Solve the wave equation,
• Get a wave function (Y)
• Y shape and size of space electron occupies
• (95 of the time, usually)
• Y an orbital

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• The wave equation yields three quantum numbers
• n, l, m

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Principal Quantum Number

• n
• n 1, 2, 3, 4, 5, 6,...
• n ? size and energy level of orbital

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Angular Momentum Quantum Number

• l
• l 0, 1, 2,..., (n-1)
• (subshell number)
• l ? shape of orbital

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Subshells

• subshell no. 0 1 2 3
• notation s p d f

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Magnetic Quantum Number

• m
• m - l to l
• m ? orientation of orbital

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Example 1

• if n1,
• l 0 only (an s-orbital)
• and
• m 0 only (1 orientation only)

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1s Orbital
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Example 2

• if n 2,
• l 0 (an s-orbital)
• or
• l 1 (a p-orbital)

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2s Orbital
node
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if l 1, m -1 or 0 or 1

• recall that l 1 implies a p-orbital
• thus, there are three p-orbitals
• they differ only in orientation

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p orbital
Nucleus
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Three p orbitals of one atom
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Example 3

• if n3,
• l 0 or l 1
• or
• l 2 (a d-orbital)
• ml -2, -1, 0, 1 or 2
• (i.e. five d-orbitals)

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Example 4

• if n4,
• l 0 or 1 or 2
• or
• l 3 (an f-orbital)
• ml -3, -2, -1, 0, 1, 2 or 3
• (i.e. 7 f-orbitals)

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Summary

• 1 type of s orbital
• 3 types of p orbital
• 5 types of d orbital
• 7 types of f orbital

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There is a fourth quantum number

• spin, ms
• ms 1/2 or -1/2
• (up or down)

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Paulis Exclusion Principle

• no two electrons in an atom have the same four
  quantum numbers

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Filling Orbitals with Electrons

• Aufbau - filling up
• put two electrons in each type
• of each orbital (one of each spin)

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Filling Orbitals with Electrons

• Hydrogen
• one electron in the 1s orbital
• electronic configuration is 1s1

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Filling Orbitals with Electrons

• Helium
• two electrons in the 1s orbital
• electronic configuration is 1s2
• (first shell complete)

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Filling Orbitals with Electrons

• Lithium
• two electrons in the 1s orbital,
• then one in the 2s orbital
• electronic configuration is 1s22s1
• or He 2s1

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Filling Orbitals with Electrons

• Beryllium
• 1s22s2
• or
• He2s2

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Filling Orbitals with Electrons

• Boron He2s22p1
• Carbon He2s22p2
• Nitrogen He2s22p3
• Oxygen He2s22p4
• Fluorine He2s22p5
• Neon He2s22p6 (second shell full)