Various Quantum Numbers

Quantum numbers are a collection of numbers used to describe the position and energy of an electron in an atom. There are four types of quantum numbers: the principal, azimuthal, magnetic, and spin quantum numbers.

They are used to determine the values of the conserved quantities in a quantum system. Electronic quantum numbers (the quantum numbers describing electrons) can be defined as a collection of numerical values that provide solutions to the Schrodinger wave equation for hydrogen atoms that are acceptable to the equation. 

These four quantum numbers can be used to completely describe all of the characteristics of a given electron belonging to an atom; the numbers are as follows:

• The principal quantum number is denoted by the letter ‘n’.
• The quantum number of orbital angular momentum (also known as azimuthal quantum number) is denoted by the letter ‘l’.
• The magnetic quantum number is denoted by the symbol ‘ml’
• The electron spin quantum number is represented by the symbol ‘ms’.
• Electronic Quantum Numbers are a type of quantum number that can be generated electronically.
• the four quantum numbers that describe the behaviour of a particle

When it comes to describing the characteristics of an electron in accordance with the Schrodinger wave equation, a total of four quantum numbers are employed. Each of the four quantum numbers that describe the unique quantum state of an electron in atomic physics is described briefly in the following section, which includes a brief description of each number.

Principal Quantum Number

• The Principal Quantum Number is a number that represents the fundamental nature of the universe. The symbol ‘n’ is used to represent the principal quantum numbers. They are used to denote the atom’s primary electron shell or shells.
• Because the principal quantum number describes the most probable 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, and vice versa (which, in turn, implies a greater atomic size).
• Integers with positive values equal to or greater than one can be used as the principal quantum number’s value, as long as they are divisible by one. If the number n=1 is used to represent an atom’s innermost electron shell, it corresponds to the lowest possible energy state (also known as the ground state) of an electron.
• Consequently, it can be seen that the principal quantum number, n, cannot have a negative value or equal to zero because an atom cannot have a negative value or no value for its principal shell, as can be seen in the example above.
• Observe that when a given electron is infused with energy (in an excited state), the electron jumps from one principle shell to a higher principle shell, thereby increasing the value of n. In a similar manner, when electrons lose energy, they jump back into lower shells, lowering the value of n in the process.
• The term “absorption” refers to the increase in the value of n for an electron, with the emphasis on the photons of energy that are being absorbed by the electron. Similar to this, when the value of n for an electron decreases, the electrons emit their stored energy; this is referred to as emission.

Azimuthal Quantum Number (Orbital Angular Momentum Quantum Number)

• Azimuthal Quantum Number is a quantum number that is oriented in the azimuthal direction (Orbital Angular Momentum Quantum Number)
• The azimuthal quantum number (or orbital angular momentum) describes the shape of an orbital in terms of its angular momentum. It is represented by the letter ‘l’ and its numerical value is equal to the total number of angular nodes in the orbital plane.
• A value of the azimuthal quantum number can indicate either an s, p, d, or f subshell, each of which has a different shape than the others. In this case, the value of the azimuthal quantum number is determined by the value of the principal quantum number, i.e., the value of the azimuthal quantum number ranges between 0 and 1. (n-1).
• The azimuthal quantum number, for example, can take on the values 0, 1, and 2 if the number n is equal to three. When l=0, the resulting subshell is ‘s’ subshell, which is the default. Similarly, when l=1 and l=2, the resulting subshells are denoted by the letters ‘p’ and ‘d’ (respectively). As a result, if n=3, the three possible subshells are 3s, 3p, and 3d, respectively.
• Another example is where the value of n is 5, and the possible values of l are 0, 1, 2, 3, and 4. In this case, the possible values of l are 0, 1, 2, 3, and 4. If l = 3, then there are a total of three angular nodes in the atom, which is the case for most atoms.

Quantum Numbers derived from the Principal and Azimuthal Quantum Numbers

It is reasonable to conclude that the ‘2d’ orbital cannot exist because the value of ‘l’ is always less than the value of ‘n’, as shown in the diagram.

Magnetic Quantum Number

• The Magnetic Quantum Number is a number that has a magnetic field around it.
• The magnetic quantum number determines the total number of orbitals in a subshell as well as the orientation of the orbitals in the subshell, among other things. A measure of it is denoted by the symbol ml. In this case, the angular momentum of the orbital is projected along a given direction, and this number represents the result of that projection.
• The value of the magnetic quantum number is dependent on the value of the azimuthal (or orbital angular momentum) quantum number, which is in turn dependent on the value of the magnetic quantum number. For a given value of l, the value of ml can be found anywhere in the range -l to +l by looking at the graph. As a result, the value of n has an indirect influence on it.

For example, if the magnetic quantum number of an atom is -3, -2, -1, 0, +1, +2, and +3 in an atom, the possible values of the magnetic quantum number are -3, -2, -1, 0, +1, +2, and +3.

• The value of the azimuthal quantum number corresponds to the number of orbitals (2l + 1).
• The total number of orbitals in a given subshell is a function of the ‘l’ value assigned to each orbital in that subshell. It can be calculated using the formula (2l + 1). For example, the ‘3d’ subshell (n=3, l=2) contains 5 orbitals (2*2 + 1), while the ‘2d’ subshell (n=3, l=2) contains 4. Each orbital has the capacity to hold two electrons. As a result, the third subshell has a total capacity of ten electrons.
• Electron Spin Quantum Number is a number that describes the spin of an electron.The electron spin quantum number is unaffected by the values of n, l, and ml, and is therefore unambiguous. The value of this number, which is denoted by the symbol ms, provides information about the direction in which the electron is spinning.
• It is possible to determine the direction in which an electron is spinning by looking at the value of ms. It is possible to have an electron spin quantum number that is between +1/2 and -1/2.
• The positive value of ms indicates that the electron has an upward spin, which is also referred to as ‘spin up,’ and is denoted by the symbol ‘spin up’. If ms is negative, the electron in question is said to have a downward spin, also known as a ‘spin down’,  which is represented by the symbol.
• The value of the electron spin quantum number determines whether or not the atom in question has the ability to generate a magnetic field in its surroundings. The value of ms can be approximated by the number +1/2 or -1/2.

Conclusion 

Quantum numbers are essential because they may be used to figure out an atom’s electron configuration and where its electrons are most likely to be found. Other properties of atoms, such as ionisation energy and atomic radius, are also understood using quantum numbers.