3.4 Quantum Numbers

### 4 quantum numbers, can be used to describe:

the spectrum lines emitted by excited electrons

the magnetic properties of electrons

the arrangement of electrons in their orbital

the relationship between the electron structure of the atom and its placement on the periodic table

**The Principal Quantum Number (n)**energy levels in an atom may be called shells

Bohr identified the shell number as the principle quantum #

describes the size and energy of an orbital

only integers

**The Secondary Quantum Number (l)**Arnold Sommerfield & Peter Debye (1951) to explain the results of high resolution line in spectra

Very small energy steps (sub levels) within the main energy level

Describe the shape of the electron orbital

The number of sub levels is equal to the value of n ( n = 3, then 3 sub levels)

n = 3, l = 0, 1, 2

s: l=0

p: l=1

d: l=2

f: l=3

**The Magnetic Quantum Number (ml)**Explains the orientation of the electron orbital

Orbitals may have the same energy level and shape, but different orientation (exist at various angles)

Valued at integers from +l to -l, including 0

For example, if l = 1, then ml = +1, 0, -1

This means there are 3 different p orbitals.

**The Spin Quantum Number (ms)**Wolfang Pauli (1925) to explain the Zeeman effect

Since charged particles create magnetic fields when vibrating, electrons must be spinning on axes

Limited to +1/2 or -1/2

An opposite pair of electrons spin in a stable way to produce no magnetic property (they cancel each other out), but an unpaired electron can be affected by a magnetic field.

## Rules of Quantum Numbers

**Pauli Exclusion Principle**No two electrons in an atom can have the same 4 quantum numbers

Each orbital may only hold 2 electrons, each with opposite spins!

**Aufbau Principle**Electrons are placed into orbitals by filling the lowest energy orbitals first

**Hund’s Rule**When several orbitals are at the same level of energy, one electron is placed into each of the orbitals, before a second electron is added

# 3.4 Quantum Numbers

### 4 quantum numbers, can be used to describe:

the spectrum lines emitted by excited electrons

the magnetic properties of electrons

the arrangement of electrons in their orbital

the relationship between the electron structure of the atom and its placement on the periodic table

**The Principal Quantum Number (n)**energy levels in an atom may be called shells

Bohr identified the shell number as the principle quantum #

describes the size and energy of an orbital

only integers

**The Secondary Quantum Number (l)**Arnold Sommerfield & Peter Debye (1951) to explain the results of high resolution line in spectra

Very small energy steps (sub levels) within the main energy level

Describe the shape of the electron orbital

The number of sub levels is equal to the value of n ( n = 3, then 3 sub levels)

n = 3, l = 0, 1, 2

s: l=0

p: l=1

d: l=2

f: l=3

**The Magnetic Quantum Number (ml)**Explains the orientation of the electron orbital

Orbitals may have the same energy level and shape, but different orientation (exist at various angles)

Valued at integers from +l to -l, including 0

For example, if l = 1, then ml = +1, 0, -1

This means there are 3 different p orbitals.

**The Spin Quantum Number (ms)**Wolfang Pauli (1925) to explain the Zeeman effect

Since charged particles create magnetic fields when vibrating, electrons must be spinning on axes

Limited to +1/2 or -1/2

An opposite pair of electrons spin in a stable way to produce no magnetic property (they cancel each other out), but an unpaired electron can be affected by a magnetic field.

## Rules of Quantum Numbers

**Pauli Exclusion Principle**No two electrons in an atom can have the same 4 quantum numbers

Each orbital may only hold 2 electrons, each with opposite spins!

**Aufbau Principle**Electrons are placed into orbitals by filling the lowest energy orbitals first

**Hund’s Rule**When several orbitals are at the same level of energy, one electron is placed into each of the orbitals, before a second electron is added