5.111 Lecture Summary #7 Wednesday, September 17, 2014
Readings for today: Section 1.12 – Orbital Energies (of many-electron atoms), Section 1.13
– The Building-Up Principle. (Same sections in 5th and 4th ed.)
Read for Lecture #8: Section 1.14 – Electronic Structure and the Periodic Table, Section
1.15, 1.16, 1.17, 1.18, and 1.20 - The Periodicity of Atomic Properties. (Same sections in 5th
and 4th ed.)
_______________________________________________________________________________
Topics: Multi-Electron Atoms
I. Wavefunctions and Binding Energies for Multi-electron Atoms
II. Electron Configurations
________________________________________________________________________________
I. WAVEFUNCTIONS AND BINDING ENERGIES FOR MULTIELECTRON ATOMS
The Schrödinger equation correctly describes the electronic structure for all atoms.
Multi-electron orbitals are similar in shape and have the same nodal structure as
corresponding hydrogen one-electron orbitals.
However, there are important differences in thinking about multi-electron
binding energies! All orbitals in a multi-electron atom are lower in energy
( ) than the corresponding orbital in a hydrogen atom.
The lower energy results in multi-electron atoms results from a higher Z--- a stronger pull
from the nucleus.
1
, The principal quantum number, n, is no longer the sole determining factor for the orbital
energies of multi-electron atoms. Binding energy now depends on and .
For -electron atoms For -electron atoms
Where Zeff is the effective charge experienced by the electron in the n,l
state. Zeff the same as Z for the nucleus.
Zeff differs from Z because of .
SHIELDING and Zeff
To illustrate the effect of shielding, consider the two extreme shielding situations possible
for the He atom (Z = 2).
Extreme CASE A for He: Extreme shielding
Electron #1
e-
Electron #2
e-
Z= 2
He nucleus (charge = )
Electron #2 maximally shields electron #1 from the (+) charge of the He nucleus
Electron #1 experiences a force on average of Zeff = , not Zeff = +2e.
The energy of electron #1 is that of an electron in an H (1-electron) atom.
2
Readings for today: Section 1.12 – Orbital Energies (of many-electron atoms), Section 1.13
– The Building-Up Principle. (Same sections in 5th and 4th ed.)
Read for Lecture #8: Section 1.14 – Electronic Structure and the Periodic Table, Section
1.15, 1.16, 1.17, 1.18, and 1.20 - The Periodicity of Atomic Properties. (Same sections in 5th
and 4th ed.)
_______________________________________________________________________________
Topics: Multi-Electron Atoms
I. Wavefunctions and Binding Energies for Multi-electron Atoms
II. Electron Configurations
________________________________________________________________________________
I. WAVEFUNCTIONS AND BINDING ENERGIES FOR MULTIELECTRON ATOMS
The Schrödinger equation correctly describes the electronic structure for all atoms.
Multi-electron orbitals are similar in shape and have the same nodal structure as
corresponding hydrogen one-electron orbitals.
However, there are important differences in thinking about multi-electron
binding energies! All orbitals in a multi-electron atom are lower in energy
( ) than the corresponding orbital in a hydrogen atom.
The lower energy results in multi-electron atoms results from a higher Z--- a stronger pull
from the nucleus.
1
, The principal quantum number, n, is no longer the sole determining factor for the orbital
energies of multi-electron atoms. Binding energy now depends on and .
For -electron atoms For -electron atoms
Where Zeff is the effective charge experienced by the electron in the n,l
state. Zeff the same as Z for the nucleus.
Zeff differs from Z because of .
SHIELDING and Zeff
To illustrate the effect of shielding, consider the two extreme shielding situations possible
for the He atom (Z = 2).
Extreme CASE A for He: Extreme shielding
Electron #1
e-
Electron #2
e-
Z= 2
He nucleus (charge = )
Electron #2 maximally shields electron #1 from the (+) charge of the He nucleus
Electron #1 experiences a force on average of Zeff = , not Zeff = +2e.
The energy of electron #1 is that of an electron in an H (1-electron) atom.
2
