Types of Quantum Numbers

Four quantum numbers are used to fully describe all the characteristics of an electron in an atom. These quantum numbers are:

• Principal Quantum Number (n)
• Azimuthal Quantum Number (l)
• Magnetic Quantum Number (m_l)
• Electron Spin Quantum Number (s)

Principal Quantum Number (n)

The symbol ‘n’ represents the principal quantum numbers. They denote the atom’s primary electron shell. Because it describes the most likely distance between the nucleus and the electrons, a larger value of the principal quantum number implies a greater distance between the electron and the nucleus (which, in turn, implies a greater atomic size).

• The principal quantum number’s value can be any integer with a positive value equal to or greater than one. The value n=1 denotes an atom’s innermost electron shell, which corresponds to an electron’s lowest energy state (or ground state). 
• As a result, the principal quantum number, n, cannot have a negative value or be equal to zero because an atom cannot have a negative value or no value for a principal shell.
• When an electron is infused with energy (excited state), the electron jumps from one principal shell to a higher shell, causing the value of n to increase.
• Similarly, as electrons lose energy, they return to lower shells, lowering the value of n. Absorption refers to the increase in the value of n for an electron, emphasizing the photons or energy absorbed by the electron. 
• Similarly, a decrease in the value of n for an electron is referred to as emission, and this is where the electrons emit their energy.

Azimuthal Quantum Number (l) – Orbital Angular Momentum Quantum Number

The azimuthal quantum number (or orbital angular momentum) describes the shape of an orbital. It is represented by the letter ‘l,’ and its value equals the total number of angular nodes in the orbital. 

• A value of the azimuthal quantum number can denote either an s, p, d, or f subshell, the shapes of which vary. 
• This value is determined by (and limited by) the value of the principal quantum number, i.e. the azimuthal quantum number ranges between 0 and (n-1).
• For example, if n = 3, the azimuthal quantum number can have three values: 0, 1, and 2. 
• When l is set to zero, the resulting subshell is an ‘s’ subshell. 
• When l=1 and l=2, the resulting subshells are ‘p’ and ‘d’ subshells, respectively (respectively). 
• As a result, when n=3, the three subshells that can exist are 3s, 3p, and 3d. In another case where n = 5, the possible values of l are 0, 1, 2, 3, and 4. If l = 3, the atom contains three angular nodes.

Magnetic Quantum Number (m_l)

The magnetic quantum number determines the total number of orbitals in a subshell as well as their orientation. It is represented by the symbol ‘m_l.’ This number represents the projection of the orbital’s angular momentum along a given axis. 

• The magnetic quantum number is determined by the azimuthal (or orbital angular momentum) quantum number. 
• For a given value of l, the value of m_l falls between -l to +l. As a result, it is indirectly dependent on the value of n. 
• For example, if n = 4 and l = 3 in an atom, the magnetic quantum number can be -3, -2, -1, 0, +1, +2, and +3. The total number of orbitals in a given subshell is determined by the orbital’s ‘l’ value. 
• It is calculated using the formula (2l + 1). The ‘3d’ subshell (n=3, l=2), for example, has 5 orbitals (2*2 + 1). Each orbital can hold two electrons. As a result, the 3d subshell can accommodate a total of 10 electrons.

Electron Spin Quantum Number (s)

The electron spin quantum number is independent of n, l, and m_l values. The value of this number, denoted by the symbol m_s, indicates the direction in which the electron is spinning. 

• The m_s value indicates the direction in which the electron is spinning. The electron spin quantum number can have values between +1/2 and -1/2. 
• A positive value of m_s denotes an upward spin on the electron, also known as spin up. 
• If m_s is negative, the electron in question is said to have a downward spin or spin down. 
• The value of the electron spin quantum number determines whether or not the atom in question can generate a magnetic field. The value of m_s can be generalized to ±½.

Quantum numbers in Chemistry, are the sets of numbers that describe an electron’s orbit and movement within an atom. When the quantum numbers of all the electrons in a given atom are added together, they must satisfy the Schrodinger equation.

Quantum numbers are the set of numbers used to describe the position and energy of an electron in an atom. There are four types of quantum numbers: principal, azimuthal, magnetic, and spin. Quantum numbers represent the values of a quantum system’s conserved quantities.

Let’s learn about all the quantum numbers in detail in this article.