The document discusses the quantum numbers used to describe electrons in atoms. There are four quantum numbers: principal (n), angular momentum (l), magnetic (ml), and electron spin (ms). The principal quantum number defines the electron's energy level and average distance from the nucleus. The angular momentum number describes the orbital shape as s, p, d, or f. The magnetic number defines the orbital orientation. Orbitals are regions where electrons are likely to be found and have different shapes depending on the angular momentum number.

1. Electronic Structure
of the Atom

2. Quantum Numbers
The set of numbers used to describe the position and energy of
the electron in an atom.
Four Quantum Numbers
• Principal Quantum Number, denoted by n.
• Angular Momentum Quantum Number (Azimuthal Quantum
Number), denoted by l.
• Magnetic Quantum Number, denoted by m sub l.
• Electron Spin Quantum Number, denoted by m sub s.

3. The Principal Quantum Number
• a. Can have the values: n = 1, 2, 3, ...
• b. Defines the location of the energy level of the given orbital
• c. Another name for the principal quantum number is the shell
number.
• d. Is related to the average distance of the electron from the nucleus
in a particular orbital; the larger the n value, the farther the average
distance of the electron from the nucleus, the higher the shell
number, and so the higher the energy level.d. Orbitals with the same
n are said to be in the same shell.

5. The Angular Momentum Quantum Number
• a. Describes the “shape” of a given orbital
• b. Can have the following values: l = 0, 1, 2, up to n – 1
Examples
n value l value
1 0
2 1
3 2
• c. It is usually designated by letters s, p, d, f, ...
Example:
If n = 3 , the angular momentum quantum number take on the following values 0, 1, and 2.
When l = 0, the resulting subshell is an ‘s’ subshell. Similarly, when l = 1 and l = 2, the resulting
subshells are ‘p’ and ‘d’ subshells (respectively). Therefore, when n = 3, the three possible subshells
are 3s, 3p, and 3d.

6. The Magnetic Quantum Number
• a. Describes the orientation of the orbital in space
• b. For a given value of l, the value of ml ranges between the interval –l
to +l.
Example:
If n = 4 and l = 3 in an atom, the possible values of the magnetic
quantum number are -3, -2, -1, 0, 1, 2, and 3.

7. The Electron Spin Quantum Number

8. Representation of Orbitals
ORBITAL
- is a region of probability where an electron can be found.
DIFFERENT SHAPES OF ORBITAL
• S ORBITAL
• D ORBITAL
• P ORBITAL
• F ORBITAL
Remember that this shape are not electrons,just regions space where
electrons can made.

9. NOTE : The L value describes the shapes of orbitals
L = 0
Describes (s) orbitals / 1 energy per level
L =1
Describes (p) orbitals / 3 energy per level
L=2
Describes (d) orbitals / 5 energy per level
L=3
Describes (s) orbital / 7 energy per level

10. Quantum Numbers and the Corresponding
Atomic Orbitals
n l ml Number of
Orbitals
Atomic Orbital
Designation
1 0 0 1 1s
2 1 -1, 0, 1 3 2s 2p

11. Atomic Orbitals are commonly designated by a combination of
numerals and letters that represent specific properties of the electrons
associated with the orbitals.

12. Energies of Orbitals
1. Orbital Energy Levels in a Hydrogen Atom
The energy of an electron in a hydrogen atom depends solely on its
principal quantum number (n).
Note: Orbitals with the same principal quantum number (n), have the same energy.
2. Orbital Energy Levels for Many-Electron Atoms
For atoms containing more than one electron (many-electron atoms), the
energy depends on other factors. These include the potention energy of repulsion
among the electrons, the attraction between the nucleus and the other electrons,
and the kinetic energies of the many electrons. Thus, the orbital energies of many-
electron atoms depend not only on principal quantum number (n) but also on
angular momentum quantum number (l).

13. Aufbau Orbitals

14. Electron Configuration
The electron configuration shows how the electrons of an atom
are distributed among the atomic orbitals.