atomic orbitals and quantum numbers - solved example

A step by step explanation of atomic orbitals and quantum numbers and interrelationships. A worked example is given.

The main topics covered in this video-tutorial are the following:
* Relationships among values of quantum numbers
*Solution to example I.2 regarding relationships among values of quantum numbers that was given in the video →

N.B.: The Quantum Mechanical Model of the atom was presented in the video →

The properties of orbitals are as follows:

Each allowed wave function ψ – known as orbital - describes the behavior of electrons with a specific energy (E).
An orbital is described by a combination of an integer and a letter, corresponding to values of 3 quantum numbers:

The principal quantum number indicated by the integers 1, 2, 3 ...This quantum number relates most directly to the size and energy of the orbital
The angular momentum quantum number, l, is indicated by the letters s, p d, f…corresponding to the values 0, 1, 2, 3… The l quantum number defines the shape of the orbital. The l quantum number can have integer values ranging from 0 to (n-1)

The magnetic quantum number, ml, relates to the orientation of the orbital in space. The ml can have integral values from –l…0…+l
The relationship among these quantum numbers is shown in the following Examples I.1 & I.2

Example I.2
Which of the following sets of quantum numbers (n, l και ml) are allowed? Which are not allowed? Explain your answer.
n=6, l=5, ml=0 b) n=3, l=3, ml=1

Answer:

a) Allowed
For n = 6 ⇒ l = 0…5 ⇒ ml = -5…+5
The values given are within the above ranges

b) Not allowed
Example I.2

a) Allowed
For n = 6 ⇒ l = 0…5 ⇒ ml = -5…+5
The values given are within the above ranges

b) Not allowed
For n = 3 ⇒ l = n -1 = 3-1 = 2 ⇒ l = 0…+2
The value of l given is l = 3 which is outside of the range of allowed values for l given above.

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