Various Quantum Numbers (Principal, Angular Momentum, and Magnetic Quantum Numbers)

Introduction

An atom is composed of a large number of orbitals that are identifiable from each other from their shape, size, and spatial perception. 

Orbital parameters are applied to define an electron’s state properly and are expressed in terms of three numbers: principal quantum number, azimuthal quantum number, magnetic quantum number, and a spin quantum number. Any numbers that designate and distinguish various atomic orbitals and electrons present in an atom are referred to as quantum numbers. 

Quantum numbers are a sequence of four numbers that can be used to gather all of the information about all of the electrons in an atom, including their energy, location, space, orbital occupied, and even the inclination of that orbital. Electronic quantum numbers can be defined as the set of numerical values that provide Schrodinger wave equation solutions for hydrogen atoms. 

It is simply a 4-digit number from which one can know the precise information about individual electrons in an atom. The information includes the location in which orbit the electron is, the space and orientation of the respective orbit, and the energy level.

The four possible quantum numbers can be used to characterise all of the aspects of an atom’s charge carriers.

Principal Quantum Number

The symbol ‘n’ refers to principal quantum numbers. They designate the atom’s fundamental electron shell. Since this indicates the most typical distance between the nucleus and the electrons, a higher value of the core quantum number signifies a greater distance between the nucleus and the electrons. Any integer with a positive value equal to or greater than one could be seen as the principal quantum number’s value. The fundamental quantum number, n, cannot be negative or equal to zero because an atom cannot have a negative or zero value for a principal shell. When an electron is infused with energy (excited state), the electron moves from one primary shell to a higher shell, adding a value of n. Similarly, when electrons lose energy, they fall to lower shells, diminishing the value of n.

Absorption corresponds to the increase in the value of n for an electron, underlining the photons of energy absorbed by the electron. Emission is the fall in the value of n for an electron, where the electrons discharge their energy.

Azimuthal Quantum Number

An electron’s azimuthal quantum number, also known as the orbital quantum number, indicates which subshell it belongs to. As a result, both its number of electronic leaps and the number of lines ascend at the same time. 

The size of an orbital is specified by the azimuthal, or we can say the orbital angular momentum quantum number. Its value is equal to the total number of angular nodes in the orbital and is signified by the symbol ‘l.’ The azimuthal quantum number can represent an s, p, d, or f subshell, each of which has multiple variations. This value can be determined and limited by the principal quantum number, i.e., the azimuthal quantum number swings between 0 and 1 (n-1).

For example, if n = 3, the azimuthal quantum number can be 0, 1, or 2. The resulting subshell is n’s subshell, respectively. When n=3, the three subshells which could be used are 3s, 3p, and 3d. In another example, the possible values of l are 0, 1, 2, 3, and 4 when the value of n is 5. There are three angular nodes in the atom if l = 3. The acceptable subshells for numerous ‘n’ and ‘l’ combinations have been described above. Since this value of ‘l’ is always less than that of ‘n,’ the ‘2d’ orbital has been unable to exist.

Understanding that you can only have one value for the first shell, say K, n = 1, i.e. l = 0; you can have two values for the second shell, say L, n = 2, i.e. l = 0 and 1; and three values for the third shell, say M, n = 3, i.e. l = 0, 1, and 2. 

Magnetic Quantum Number

The magnetic quantum number, abbreviated as m, specifies the orientation of molecular orbitals in space. It is measured by the value of l. Hence, the total number of magnetic quantum numbers can be (2l + 1). 

The magnetic quantum number determines the overall number of orbitals in a subshell along with relative orientation. The symbol ‘ml‘ can be used to signify it. These values indicate the projection of the orbital angular momentum with an accurate output. The azimuthal quantum number or we could say the orbital angular momentum quantum number includes the amount of the magnetic quantum number. The value of ml for a specific significance of l seems to be in the range of -l to +l. As a response, it is indirectly determined by the value of n. Every respective P orbital has a similar energy level in the absence of a magnetic field. Similarly, every d and f orbits have the same energy in the absence of an external magnetic field, and these types of orbits are termed degenerate orbitals. But in the case of applied external magnetic fields, the degenerate orbitals acquire slightly different energies compared to their neighbouring orbitals. 

For example, if n = 4 and l = 3 in an atom, the magnetic quantum number might be -3, -2, -1, 0, +1, +2, or +3.

Spin Quantum Number

An atom’s electrons not only traverse around but also spin over their own axis. This number shows the location for which an electron in an orbital is spinning. It is symbolised by the letters s or ms, and that’s because electrons can spin in either a clockwise or anti-clockwise direction. A given value of m, s can only have two values: -1 or +1, or as two arrows moving in opposite ways. This quantum number assists in the description of the substance’s magnetic characteristics. 

A spinning electron operates like a microscopic magnet with a distinctive magnetic field. While two electrons share an orbital, their magnetic movements oppose and cancel one other. When the net magnetic field tends to zero then, that substance could also be known as a Diamagnetic substance. And in paramagnetic material, the net magnetic file does not tend to zero. 

Conclusion 

The movement and the path followed by each electron are described by using quantum numbers. Each electron in an atom has unique set of quantum numbers. Principal quantum number indicates the most typical distance between the nucleus and the electrons, Azimuthal quantum no. indicates which subshell electron belongs to, Magnetic quantum number determines the overall number of orbitals in a subshell along with relative orientation and Spin quantum number tells about angular momentum of an electron.