Atomic
Structure
• The Schrödinger equation, sometimes called the
Schrödinger wave equation, is a partial differential
equation. It uses the concept of energy conservation
(Kinetic Energy + Potential Energy = Total Energy) to
obtain information about the behavior of an electron bound
to a nucleus.
• It does this by allowing an electron's wave function, Ψ, to
be calculated.
• Solving the Schrödinger equation gives us Ψ and Ψ2.
With these we get the quantum numbers and the
shapes and orientations of orbitals that characterize
electrons in an atom or molecule.
Px
Pz
Py
1) The principal quantum number (n)
• The principal quantum number n describes the average
distance of the orbital from the nucleus — and the
energy of the electron in an atom.
• It can have only positive integer (whole number)
values: 1, 2, 3, 4, and so on.
• The larger the value of n, the higher the energy and the
larger the orbital, or electron shell.
2) The angular momentum quantum number (l)
• Describes the shape of the orbital, and the shape is
limited by the principal quantum number n:
• The angular momentum quantum number l can have
positive integer values from (0) to (n – 1).
• For example, if the n value is 3, three values are
allowed for l: 0, 1, and 2.
• The value of l defines the shape of the orbital, and the
value of n defines the size.
• Orbitals that have the same value of n but different
values of l are called subshells.
• These subshells are given different letters to help
chemists distinguish them from each other.
• When chemists describe one particular subshell in an
atom, they can use both the n value and the subshell
letter: 2p, 3d, and so on.
• Normally, a subshell value of 4 is the largest needed
to describe a particular subshell
3) The magnetic quantum number (ml)
• It describes how the various orbitals are oriented in space.
• The value of ml depends on the value of l.
• The values allowed are integers from (–l) to (0) to (+l).
• For example, if the value of l = 1 (p orbital), you can write
three values for ml: –1, 0, and +1.
• This means that there are three different p orbitals for the same
subshell
• The orbitals have the same energy but different
orientations in space.
• Notice that the three p orbitals correspond to ml values
of –1, 0, and +1, oriented along the x, y, and z axes.
• Figure (a) shows the shape of s
orbitals.
• There are two s orbitals — one for
energy level 1(1s) and the other
for energy level 2 (2s).
• S orbitals are spherical with the
nucleus at the center.
• Notice that the 2s orbital is larger
in diameter than the 1s orbital.
• In large atoms, the1s orbital is Figure (a)
nestled inside the 2s, just like the
2p is nestled inside the 3p.
Figure (b) shows the shape of p orbitals.
Figure (b)
Figure (c) shows
the shape of d
orbitals.
Figure (c)
• Notes for the different kinds of orbitals:
1) Each kind of orbital has a different "shape", and the
shapes get progressively more complex.
2) It can also be seen that:
• The s-kind has only one orbital
• The p-kind has three orbitals
• The d-kind has five orbitals *Remember ml
• Each orbital can hold only two electrons.
• This means that the 1s, 2s, 3s, 4s, etc., can each
hold two electrons because they each have only one orbital.
• The 2p, 3p, 4p, etc., can each hold six electrons because they
each have three orbitals, that can hold two electrons each
(3*2=6).
• The 3d, 4d etc., can each hold ten electrons, because they each
have five orbitals, and each orbital can hold two electrons
(5*2=10).
http://www.youtube.com/watch?v=K-jNgq16jEY
4) The spin quantum number (ms)
• This one describes the direction the electron is spinning in
a magnetic field: either clockwise or counter clockwise.
• Only two values are allowed for ms: +1⁄2 or –1⁄2.
• For each orbital in the subshell, there can be only two
electrons, one with a spin of +1⁄2 and another with a spin
of –1⁄2.
https://www.youtube.com/watch?v=A0-jy-uCwQk
Pauli Exclusion Principle
• The Pauli Exclusion Principle states that, in an atom or
molecule, no two electrons can have the same four
electronic quantum numbers.
• As an orbital can contain a maximum of only two
electrons, the two electrons must have opposing spins.
Summary of the quantum numbers
• There’s an energy difference in the major energy levels
(energy level 2 is higher in energy than energy level 1),
• But there’s also a difference in the energies of the different
subshells within an energy level.
• At energy level 2, both s and p subshells are present; but
the 2s is lower in energy than the 2p.
• The three orbitals of the 2p subshell have the same
energy.
• Likewise, the five orbitals of the d subshell have the
same energy.
• https://www.youtube.com/watch?v=0Bt6RPP2ANI&t=628s
