Quantum Numbers. principal quantum number: n. angular momentum quantum number: l (azimuthal) magnetic quantum number: m l
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1 Quantum Numbers
2 Quantum Numbers principal quantum number: n angular momentum quantum number: l (azimuthal) magnetic quantum number: m l
3 Principal quantum number: n related to size and energy of orbital shells: integral values: 1, 2, 3,... higher n the electron is farther from nucleus the electron less strongly bound by nucleus (higher energy potential)
4 Angular momentum quantum number: l related to shape of orbital subshells: integral values: 0, 1, 2,, n - 1 l = 0: s orbital l = 1: p orbital l = 2: d orbital l = 3: f orbital
5 Relation of n and l n = 1 n = 2 n = 3 n = 4 l = 0 l = 0, 1 l = 0, 1, 2 l = 0, 1, 2, 3 1s 2s, 2p 3s, 3p, 3d 4s, 4p, 4d, 4f
6 Magnetic quantum number: m l related to the three-dimensional orientation of orbital in space integral values between l and -l
7 Relation of l and m l s: l = 0 m l = 0 p: l = 1 m l = -1, 0, 1 d: l = 2 m l = -2, -1, 0, 1, 2 f: l = 3 m l = -3, -2, -1, 0, 1, 2, 3
8 Probability distribution for an electron in a 1s orbital is spherical
9 Probability of finding an electron in a 1s orbital at a certain distance on a line originating at the nucleus Electron density Distance from nucleus
10 Boundary surface encloses 90% of the total electron probability
11 Boundary surface encloses 90% of the total electron probability Chemists approximate an orbital by the volume enclosed by the boundary surface
12 s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n Pearson Education, Inc. Electronic Structure of Atoms
13 p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them Pearson Education, Inc. Electronic Structure of Atoms
14 2p x orbital boundary surface lobes z y x where the electron is not yz plane is a nodal plane
15 2p y orbital boundary surface z y x
16 2p z orbital boundary surface z y x
17 d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center Pearson Education, Inc. Electronic Structure of Atoms
18
19
20 Atomic Orbitals
21 each orbital is characterized by a unique set of quantum numbers principal quantum number: angular momentum quantum number: magnetic quantum number: n l m l ( 1, 0, 0 ) 1s
22 each orbital is characterized by a unique set of quantum numbers principal quantum number: angular momentum quantum number: magnetic quantum number: n l m l ( 2, 1, 1 ) 2px
23 each orbital is characterized by a unique set of quantum numbers principal quantum number: angular momentum quantum number: magnetic quantum number: n l m l ( 2, 1, 0 ) 2py
24 each orbital is characterized by a unique set of quantum numbers principal quantum number: angular momentum quantum number: magnetic quantum number: n l m l ( 2, 1, -1 ) 2pz
25 each orbital is characterized by a unique set of quantum numbers principal quantum number: angular momentum quantum number: magnetic quantum number: n l m l ( 3, 2, 1 ) 3dx 2 - y 2
26 energies of hydrogen orbitals for the hydrogen atom, all orbitals with the same principal quantum number have the same energy i.e., they are degenerate
27 1s Potential Energy Orbital energy levels in the hydrogen atom
28 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Orbital energy levels in the hydrogen atom
29 energies of multi-electron orbitals for a many-electron atom, the energy depends on both the principal quantum number and the angular momentum quantum number i.e., each subshell represents a different energy in a multi-electron system
30 5s 4s 4p 4d 3d 3s 3p 2s 2p 1s Orbital energy levels in a many-electron atom
31 Shielding Effect in a many-electron atom, electrons in the 1s orbital shield the electrons located in the 2s and 2p orbitals from the electrostatic attraction of the protons in the nucleus 2s electron density is greater near the nucleus than 2p electron density 2s orbital is said to be more penetrating and is less shielded than the 2p
32 32
33 Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate Pearson Education, Inc. Electronic Structure of Atoms
34 Energies of Orbitals 2012 Pearson Education, Inc. As the number of electrons increases, though, so does the repulsion between them. Therefore, in manyelectron atoms, orbitals on the same energy level are no longer degenerate. Electronic Structure of Atoms
Chapter 6. of Atoms. Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten
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