French physicist Louis de Broglie initially proposed that electrons behave as both particles and waves in 1924. Erwin Schrödinger further developed this idea with a wave equation to describe electron behavior in 1926. Quantum theory explains the mathematical description of electron wave properties and orbital probabilities, revolutionizing the understanding of atomic structure.

1. QUANTUM MODEL
OF THE ATOMS

2. IN 1924, FRENCH PHYSICIST LOUIS DE BROGLIE
INITIALLY THOUGHT THAT ELECTRONS BEHAVE
BOTH LIKE A WAVE AND A PARTICLE. HOWEVER,
HE LATER EMPHASIZED THAT ELECTRONS (AS IN
BOHR'S QUANTIZED ORBIT) BEHAVE MORE LIKE A
WAVE.
HENCE, DE BROGLIE PROPOSED THAT ELECTRONS BECONSIDERED
AS WAVES CONFINED IN THE SPACE SURROUNDING AN ATOMIC
NUCLEUS. THESE WAVE-LIKE PROPERTIES OF ELECTRONS WERE
LATER SUPPORTED BY OTHER SCIENTIFIC STUDIES SUCH AS THE
LIGHT DIFFRACTION EXPERIMENTS.
LIGHT HAS BOTH WAVE-LIKE AND PARTICLE-LIKEPROPERTIES. THIS CONCEPT WAS
REVEALED FROM THE STUDY OF THE PHOTOELECTRIC EFFECT AND HYDROGEN'S
LINE EMISSION SPECTRUM.

3. ERWIN
SCHRÖDINGER
WERNER
HEISENBERG
FURTHERMORE, AUSTRIAN PHYSICIST ERWIN SCHRÖDINGER
DEVELOPED, IN 1926, A MATHEMATICAL EQUATION THAT
DESCRIBES THIS BEHAVIOR OF ELECTRONS.
IN 1927, GERMAN PHYSICIST WERNER HEISENBERG STILL LOOKED INTO
THE POSSIBILITY THAT ELECTRONS BEHAVEBOTH AS A WAVE AND A
PARTICLE. IN HIS UNCERTAINTY PRINCIPLE, HEISENBERG STATED THAT IT
IS IMPOSSIBLE TO SIMULTANEOUSLY DETERMINE BOTH THE POSITION AND
THE MOMENTUM (EQUAL TO PRODUCT OF MASS AND VELOCITY) OF AN
ELECTRON. HEISENBERG'S UNCERTAINTY PRINCIPLE AND SCHRÖDINGER'S
WAVE EQUATION BECAME THE ADVENT OF QUANTUM THEORY.

4. QUANTUM THEORY
THE QUANTUM THEORY EXPLAINS THE MATHEMATICAL DESCRIPTION OF THE WAVE PROPERTIES OF ELECTRONS
AND OTHER SMALL PARTICLES. IT SUGGESTS THE PROBABILITY OF FINDING AN ELECTRON AT A GIVEN PLACE
AROUND THE NUCLEUS.
RECALL THAT THIS WAS A SIMILAR OBSERVATION OF BOHR-THAT ELECTRONS DO NOT MOVE JUSTANYWHERE
AROUND THE NUCLEUS; INSTEAD THEY EXIST IN CERTAIN REGIONS CALLED ORBITALS.
AN ORBITAL IS A THREE-DIMENSIONAL REGION SURROUNDING THE NUCLEUS AND
REPRESENTSTHE PROBABLE LOCATION OF THE ELECTRONS. NOTE THAT IT IS DIFFERENT
FROM AN ORBIT, WHICH IS THE PATH OF A REVOLVING OBJECT.

5. QUANTUM NUMBERS
QUANTUM NUMBERS DESCRIBE THE ATOMIC ORBITALS AS WELL AS THE PROPERTIES OF
THE ELECTRONS IN THOSE ORBITALS. THESE ARE THE PRINCIPAL, AZIMUTHAL,
MAGNETIC, AND SPIN QUANTUM NUMBERS.

6. THE PRINCIPAL QUANTUM NUMBER (W) INDICATES THE SIZE OF THE ORBITAL. THE BIGGER THE W IS,
THE GREATER IS THE AVERAGE DISTANCE OF AN ELECTRON IN THE ORBITAL FROM THE NUCLEUS AND
THUS, THE LARGER THE ORBITAL AND THE ATOM. THE PRINCIPAL QUANTUM NUMBER ALSO INDICATES
THE MAIN ENERGY LEVEL OCCUPIED BYAN ELECTRON, AND TAKES ON POSITIVE INTEGERS (1, 2, 3, AND
SO ON) AS VALUES.
FOR EXAMPLE, AN ELECTRON WITH N = 1OCCUPIES THE FIRST ENERGY LEVELCLOSEST TO THE
NUCLEUS. MORE THAN ONE ELECTRON CAN OCCUPY THE SAME ENERGY LEVEL IN THE SAME SHELL. A
SHELL IS COMPOSED OF A SET OF ORBITALS THAT HAVE THE SAME PRINCIPAL QUANTUM NUMBER.
PRINCIPLE QUANTUM NUMBERS

7. THE AZIMUTHAL QUANTUM NUMBER (L), ALSO KNOWN AS ANGULAR
MOMENTUM QUANTUM NUMBER, CORRESPONDS TO THE SHAPE OF THE
ORBITAL. ALLOWED VALUES FOR INCLUDE 0 AND ALL POSITIVE INTEGERS
LESS THAN OR EQUAL TO -1.
FOR EXAMPLE, AN N = 1 DENOTES A SPECIFIC ORBITAL SHAPE
CORRESPONDING TO L=0. AN N = 2 MAY HAVE ONE OF TWO ORBITAL
SHAPES CORRESPONDING TO L=0 AND L=1. AS SHOWN IN TABLE 2-1,
LETTERS ARE ASSIGNED TO THE ORBITALS DEPENDING ON THE VALUES.
THEREFORE, AN L=0 CORRESPONDS TO AN S ORBITAL; = 1 MEANS A P
ORBITAL; AND SO ON.
AZIMUTHAL QUANTUM NUMBERS

9. one or more orbitals with the same values of n an l are known as subshell.
For example, the shell with n=2 two subshells (l=0 and l=1. These subshells are
referred tp as the 2s and 2p subshells. the number “2” refers to n, while s and p refer
to the two values of l. each subshell can accommodate only certain number of
electron as indicated in table 2-1.

10. Magnetic Quantum Number
The magnetic quantum number (m l ) indicates the orientation of an orbital around the nucleus.
for a particular value of l, there will be (2l+1) possible values of m l. Hence, the values for m l are
integers from -l to +l , including 0. for example, i l = 0, only one value for ml is possible : that is ml=0.
If l=1, there are [2l +1 = 3] possible values of ml, which are -1, 0 and +1.
The number of ml values also gives an idea about the number of orientations of orbital belonging
to a particular subshell. for instance, for a p orbital with l=1, the three possible ml values (-1,0,+1 )
imply that there are three orientations of the p orbital around the nucleus.

11. Spin Quantum Numbers
The spin quantum number (ms) indicates the spin of the electron
and may have only two possible values, +1/2 and - 1/2. The
orientation is normally upward or downward .

14. Austrian physicist renowned for his contributions to
quantum mechanics
Proposed the Quantum Model in the 1920s
ERWIN SCHRÖDINGER
1887 - 1961
Quantum mechanics provides a comprehensive understanding of
electron behavior
Schrödinger's model successfully explains multi-electron atoms
Quantum mechanics is the foundation of modern atomic theory