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Quantum numbers are a set of constant values. Quantum numbers, also known as electronic quantum numbers, are numerical values assigned to electrons that offer solutions to the Schrodinger wave equation for hydrogen atoms. The Schrodinger equation must be satisfied when combining the quantum numbers of all electrons in a particular atom. The collection of numbers can define the location, energy, and direction of an electron in an atom. 

Types of Quantum Numbers 

The four-quantum number completely characterizes or offers comprehensive information about an electron in an atom. The quantum numbers are: 

The Principal Quantum Number (n)  

Azimuthal Quantum Number (l)  

Magnetic Quantum Number (ml)  

Spin Quantum Number of Electrons (s)  

Principal Quantum Number 

The principal quantum numbers are represented by the sign ‘n’. They represent an atom’s primary electron shell. The larger the primary quantum number's value, the greater the distance between the nucleus and electrons, and thus the atomic size. 

The principal quantum number value can be any positive integer greater than or equal to one. The number n=1 signifies an atom’s innermost electron shell, which corresponds to the lowest energy state of an electron. 

As an atom cannot have a negative value, the principal quantum number cannot have a negative value. 

The value of the principal quantum number will be increased if an electron observes energy and jumps from one shell to a higher shell. 

Also, when electrons lose energy, they return to lower shells, decreasing the value of n. 

Absorption is the rise in the value of n for an electron that highlights the photons or energy absorbed. Similarly, the drop in the value of n for an electron is known as emission, and here is where the electrons emit their energy. 

Azimuthal Quantum Number 

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

Azimuthal Quantum Number Formula and Explanation: 

An azimuthal quantum number value can represent an s, p, d, or f subshell in many configurations. 

Its value is determined (and restricted by) the value of the principal quantum number, which spans between 0 and 1. (n-1). 

For example, if n = 3, the azimuthal quantum number can be one of three values: zero, one, or two. 

The resultant subshell is an ‘s’ subshell when l is set to zero. 

For l=1 and l=2, the resultant subshells are ‘p’ and ‘d,’ respectively. 

As a result, the three feasible subshells for n=3 are 3s, 3p, and 3d. In another situation when n = 5, the available values of l are zero, one, two, three, and four. The atom has three angular nodes when l = 3. 

Magnetic Quantum Number 

The magnetic quantum number defines the overall number and orientation of orbitals in a subshell. It is denoted by the symbol ‘ml‘. This value indicates the orbital’s angular momentum projected along a specified axis. Let us understand the magnetic quantum number formula and detailed explanation: 

The magnetic quantum number is determined by the azimuthal quantum number. 

The value of ml for a given l lies between -l and +l. As a result, the value of n has an indirect effect on it. 

If n = 4 and l = 3, the magnetic quantum number in an atom might be -3, -2, -1, 0, +1, +2, and +3. The orbital’s ‘l’ value determines the overall number of orbitals in a particular subshell. 

The formula (2l + 1) is used to compute it. The ‘3d’ subshell (n=3, l=2), for example, has 5 orbitals (2*2 + 1). Each orbital may accommodate two electrons. As a consequence, the 3d subshell may hold a total of 10 electrons. 

Electron Spin Quantum Number 

The values of n, l, and ml have no effect on the electron spin quantum number. The value of this number, represented by the symbol ms, represents the spin direction of the electron. 

The ms value tells which way the electron is spinning. The electron spin quantum number can range from +1/2 to -1/2. 

A positive ms value indicates that the electron has an upward spin, often known as spin, up. 

If ms is negative, the electron has a downward spin, often known as spin, down. 

The quantum number of electron spin determines whether an atom can produce a magnetic field. The value of ms can be generalized to ±1/2.