atomic orbitals and quantum numbers - worked examples

A step by step explanation of atomic orbitals and quantum numbers and interrelationships. Worked examples are given.

The main topics covered in this video-tutorial are the following:

Relationships among values of quantum numbers

Two worked examples I.1 & I.2 regarding relationships among values of quantum numbers

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.1

What is the maximum number of electrons in an atom that can have quantum numbers n=5 and l=3? Explain your answer.

Answer:

Two ways to answer this question: i) a short answer ii) a detailed explanation
i) An orbital with n=5 and l=3 is a 5f orbital. Remember that there are 7 degenerate f orbitals. Each orbital can accommodate up to 2 electrons. Therefore, the maximum number of electrons is: 7*2 = 14
Example I.1

ii) A more detailed explanation is as follows. Write down the possible combinations of n , , mL and
Remember that each quartet of quantum numbers corresponds to an electron.
Example I.1

ii) There are 14 possible combinations. Each one defines an electron  14 electrons is the max. number ia a 5f orbital.

Example I.2
What are the quantum numbers for the outermost electron of the 12Mg atom?

Answer:
Answer for this example is given in the video →

Relevant Videos: