5.111 Lecture Summary #5 Friday, September 12, 2014
Readings for today: Section 1.3 – Atomic Spectra, Section 1.7 up to equation 9b –
Wavefunctions and Energy Levels, Section 1.8 – The Principle Quantum
Number. (Same sections in 5th and 4th ed.)
Read for Lecture #6: Sections 1.9, 1.10, and 1.11 (Same sections in 4th ed.)
Assignment: Problem set #2 (due Thursday, September 18th at 5 pm).
_______________________________________________________________________________
Topics: The Schrödinger Equation and Hydrogen Atom Energy Levels
I. Binding energies of the electron to the nucleus for a hydrogen atom
II. Verification of hydrogen-atom energy levels
A. Photon emission
B. Photon absorption
________________________________________________________________________________
The Schrödinger equation is an equation of motion for particles (like electrons) that
accounts for their wave-like properties. Solutions to the Schrödinger equation indicate
possible binding energies and wavefunctions.
Energy level diagram for the H atom
Note that all binding energies are . A negative value means that the
electron is bound to the nucleus. At n=∞ (En = 0), the e- is free from the nucleus.
The lowest (most negative) energy is called the .
• The ground state is the most stable state.
• The ground state is the n = 1 state.
1
, Ionization energy (IE) is the minimum energy required to remove an electron from the nth state
of a gaseous atom, molecule or ion. (Assume ground state, n=1, unless otherwise specified.)
• En = (ionization energy) of the hydrogen atom in the nth state.
• Ionization energy is always . You always need to put energy into a
system to eject an electron.
• The IE for a hydrogen atom in the ground state = J. This means if you
put that amount of energy into a hydrogen atom in its ground state, the electron is no
longer bound to the nucleus.
• The IE for a hydrogen atom in the n = 2 (first excited state) is J.
• The IE of a hydrogen atom in the third excited state (n = ) is J.
The following equation describes the binding energy for any one-electron atom (including
ions):
where Z = atomic number
Electron is more weakly bound when n is big and more tightly when Z is big.
Atoms or ions with one electron:
H ≡ one electron atom Z = 1 (atomic number)
He+ ≡ one electron ion Z=2
Li2+ ≡ one electron ion Z=
Tb64+ ≡ one electron ion Z=
2
Readings for today: Section 1.3 – Atomic Spectra, Section 1.7 up to equation 9b –
Wavefunctions and Energy Levels, Section 1.8 – The Principle Quantum
Number. (Same sections in 5th and 4th ed.)
Read for Lecture #6: Sections 1.9, 1.10, and 1.11 (Same sections in 4th ed.)
Assignment: Problem set #2 (due Thursday, September 18th at 5 pm).
_______________________________________________________________________________
Topics: The Schrödinger Equation and Hydrogen Atom Energy Levels
I. Binding energies of the electron to the nucleus for a hydrogen atom
II. Verification of hydrogen-atom energy levels
A. Photon emission
B. Photon absorption
________________________________________________________________________________
The Schrödinger equation is an equation of motion for particles (like electrons) that
accounts for their wave-like properties. Solutions to the Schrödinger equation indicate
possible binding energies and wavefunctions.
Energy level diagram for the H atom
Note that all binding energies are . A negative value means that the
electron is bound to the nucleus. At n=∞ (En = 0), the e- is free from the nucleus.
The lowest (most negative) energy is called the .
• The ground state is the most stable state.
• The ground state is the n = 1 state.
1
, Ionization energy (IE) is the minimum energy required to remove an electron from the nth state
of a gaseous atom, molecule or ion. (Assume ground state, n=1, unless otherwise specified.)
• En = (ionization energy) of the hydrogen atom in the nth state.
• Ionization energy is always . You always need to put energy into a
system to eject an electron.
• The IE for a hydrogen atom in the ground state = J. This means if you
put that amount of energy into a hydrogen atom in its ground state, the electron is no
longer bound to the nucleus.
• The IE for a hydrogen atom in the n = 2 (first excited state) is J.
• The IE of a hydrogen atom in the third excited state (n = ) is J.
The following equation describes the binding energy for any one-electron atom (including
ions):
where Z = atomic number
Electron is more weakly bound when n is big and more tightly when Z is big.
Atoms or ions with one electron:
H ≡ one electron atom Z = 1 (atomic number)
He+ ≡ one electron ion Z=2
Li2+ ≡ one electron ion Z=
Tb64+ ≡ one electron ion Z=
2
