Calculating quantum numbers is one of the difficult concepts that students fail to understand. Today, we will see how to obtain these values without struggle.

But before that, it is good we discuss what these quantum numbers are.

Table of Contents

# What are quantum numbers?

Quantum numbers are a set of numbers used to describe the characteristics of every electron in an atom. There are usually four quantum numbers in which each electron in an atom has different quantum numbers. There can never be a situation where 2 electrons have the same quantum numbers.

These quantum numbers include:

**Principle quantum numbers (**n**)**

The principle quantum number is represented by the letter *n*. It represents the energy level to which an electron is located within an atom. The values of n can only be positive integers because the lowest energy level for every atom is 1.

n=1,2,3,4,5,6…..(only positive integers)

Electrons are usually localized in their energy level unless energy is applied. However, they can move from a ground state (lover n) to an excited state (higher n). If sufficient energy is applied, the electron will move a lower energy level to a lower energy level, such as from n=1 to n=2, and this process is called absorption.

This process is called relaxation if the electrons move from a higher to a lower energy level, such as n=3 to n=2. During excitation, an electron absorbs a certain amount of energy that is enough to move it to the excited state, while during relaxation, the same amount of energy is released.

During the relaxation of an electron, they release a certain amount of energy in a specific wavelength that is associated with a certain color. This is the process that describes spectrophotometry.

**Angular momentum quantum number (***l*)

*l*)

Angular momentum is denoted by a letter (l). It represents the orbital to which the electron belongs. The value of angular momentum depends on the principle quantum number in that; *L= n*-1.

the values of angular momentum (l) can be from 0, 1,2,3,4———-(n-1).

**Magnetic quantum numbers ***(ml*)

*(ml*)

The magnetic quantum number is represented by the letter *ml*. It represents the orientation of orbitals within a subshell. The formula for magnetic quantum numbers depends on the angular quantum numbers.

The formula is *-l* ………..0*…………+l*

This means that it takes values from negative *l* to positive *l*. the below examples will guide you more.

**Electron spin quantum numbers. (***ms*)

*ms*)

The electron spin quantum number is represented by the formula *ms*. This is used to represent the spin of an electron in an orbital. We know that an orbital can accommodate a maximum of two electrons, and they must have opposite spins. The spin of an electron can either be +1/2 or -1/2. Therefore, electrons can have either of the two values.

**A summary table for quantum numbers.**

The following table is useful in guiding you on how to calculate quantum numbers.

Number | Symbol | values |

Principle quantum number | n | 1,2,3,4 (values from 1 and above….) no negative values. |

Angular momentum quantum number | l | (n-1) values from 0 and above only) no negative values. |

Magnetic quantum number | ml | –l……0……..+l (values from negative l to positive l) |

Spin quantum number | ms | Either +1/2 or ½ ONLY |

**Examples of how to calculate quantum numbers**

**When n=4***Possible l values are: l= 3,2,1,0**Possible ml values are: Ml= +3,+2,+1,0,-1,-2,-3**Possible ms values are: Ms= +1/2 or -1/2*

*Second one *

**When n=5***Possible l values are: l= 4,3,2,1,0**Possible ml values are: Ml= +4,+3,+2,+1,0,-1,-2,-3,-4**Possible ms values are: Ms= +1/2 or -1/2*

Third

**When n=3***Possible l values are: l= ,2,1,0**Possible ml values are: Ml= +2,+1,0,-1,-2**Possible ms values are: Ms= +1/2 or -1/2*

Forth

**When n=2***Possible l values are: l= 1,0**Possible ml values are: Ml=+1,0,-1**Possible ms values are: Ms= +1/2 or -1/2*

Fifth

**When n=6***Possible l values are: l= 5,4,3,2,1,0**Possible ml values are: Ml=+5,+4,+3,+2,+1,0,-1,-2,-3,-4,-5**Possible ms values are: Ms= +1/2 or -1/2*

Sixth

- What are the accepted quantum numbers for n=4
- Possible values of n= 4
- Possible values of
*l*= 0,1,2,3 - Possible values of
*ml*= -3,-2,-1,0,+1,+2,+3 - Possible values of ms= +1/2 or -1/2

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