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Lecture 12

# CHMA10H3 Lecture Notes - Lecture 12: Azimuthal Quantum Number, Max Born, Wave Equation

Department
Chemistry
Course Code
CHMA10H3
Professor
Marco Zimmer
Lecture
12

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CHMA10- Lecture 12 (Feb. 1st)
Quantum Model of the Atom
- Quantum Mechanics: The Wave Equation
ļ Schrodinger latched onto the idea of e- as waves and in 1925 came up with differential
equation (known as Schrodinger equation) to describe an e- in an atom as a wave
ļ Schrodinger Wave Equation (more detail)
ā Describes both the particle and wave nature of the e- in a hydrogen atoms
ļ Max Born realized that he can calculate the probability density for the e- by
looking at the function š2
o š2 gives a 3D probability density plot for an electronās position in space called
orbital
o We can calculate āshapesā that represent boundaries within which an electron
should be found
o Visual representation of the atom:
ļ Each electron is described by 3 quantum numbers: n for energy, ā for
angular momentum and m for spatial orientation
- Orbitals and Quantum Numbers
ļ© Atomic Orbital: a 3D description of the probability density for a given wave function
ļ© Characterized by a set of quantum numbers which determine orbital size, energy, shape
and orientation
ļ Describes average size of the orbital and indicates the energy level
ļ n take on values of 1,2,3,4,5ā¦ (only positive integers)
ļ Numbers also correspond to letters where 1=K, 2=L, 3=M, 4=N, etcā¦
ļ In a hydrogen atom, the energy of an electron with principal quantum number n
is:
ļ ānā determines the size of this 90% boundary