Key Notes on Principal Quantum Numbers

The primary quantum number (symbolised n) is one of four quantum numbers allocated to each electron in an atom to characterise the state of that electron in quantum mechanics. It is a discrete variable since its values are natural integers. The primary quantum number was designed to distinguish between different energy levels in the semiclassical Bohr model of the atom. With the advent of modern quantum physics, the simple Bohr model was replaced by a more sophisticated theory of atomic orbitals. However, the principal quantum number is still required in current theory.

Principal Quantum numbers

• The principal quantum numbers are represented by the symbol n. They represent the main electron shell of an atom. A larger value of the primary quantum number denotes a greater distance between the nucleus and the electrons since it describes the most likely distance between the nucleus and the electrons (states a greater atomic size).
• Any integer with a positive value equal to or greater than one can be used as the principal quantum number’s value. The value n=1signifies the innermost electron shell of an atom, which corresponds to the lowest energy state of an electron (or ground state).
• As a result, the primary quantum number, n, cannot have a negative or zero value since an atom’s principal shell cannot have a negative or zero value.
• When an electron is energised and filled with energy, it goes from one primary shell to the next higher shell, increasing the value of n. When an electron loses energy, it moves to the lower shells, which lowers the value of n.
• The term “absorption” refers to an increase in the value of n for an electron, emphasising the amount of energy absorbed in the form of photons. When the value of n decreases, an electron is known as emission, and this is where the electrons expel their energy.
• Bohr is credited for laying the groundwork for orbital chemistry as we know it today. He discovered that electron orbitals represent an energy level based on their distance from the atom’s nucleus. The orbitals were given the namesK,L,M,N OR 1,2,3,4 in ascending sequence. Principal Quantum Numbers are the names given to these numbers. The state of each electron in an atom is described by the main quantum number assigned to it. It is represented by the letter n and can only take positive integer values. For the M orbital, n=3.

Quantum numbers

The route and movement of an electron within an atom are defined by quantum numbers. Aside from that, the quantum numbers of each electron in an atom are discovered to be mixed, implying that it should obey the Schrodinger equation, a mathematical formula that explains the energy and position of an electron in space and time.

The energy state of electrons is described by four numbers:

• The energy levels are expressed by the principal quantum number. The letter n stands for it.
• Angular Momentum Quantum Number: Also known as Azimuthal Quantum Number. It explains what a subshell  is used to indicate it.
• (A shell is an atom’s grouping of electrons based on their energies; a subshell is an electron pathway that moves within the shell; and orbitals are the regions of space where electrons prefer to live in an atom.)
• The orbital of a subshell is expressed by the magnetic quantum number. It’s represented by the letters ms or m.

The quantity of energy available in atoms and molecules is described by a quantum number. Furthermore, the energy state of an electron within an ion or an atom is represented by four of these numbers. Additionally, it clarifies Schrodinger’s wave equation for hydrogen atoms.

Background of Quantum Numbers

• Electrons have discrete energy levels connected with their atomic radius, according to Broglie and Bohr’s studies. A more straightforward spherical perspective was provided by this model. Furthermore, the model of Bohr and Broglie revealed the relationship between electron energy levels and their principal quantum number. However, this model does not include any numerical methods for classifying extra behaviour of an electron in space.
• Schrodinger’s equation also included three more quantum numbers to describe the behaviour of an electron in a more complicated multi-electron atom. This paradigm was the polar opposite of what Bohr and Broglie had postulated previously. Furthermore, it opened up new opportunities for quantum number study.
• Based on these two models and additional inputs from John Lennard-Jones and Slater, the Hund-Mulliken theory was created. Furthermore, throughout the history of quantum mechanics, this theory is recognised as the most famous nomenclature system. Furthermore, this nomenclature adheres to the Hund-Mulliken theory, as well as Bohr’s energy levels, spectroscopic data on electron spin, and Hund’s rule.

Conclusion

The primary quantum number was designed to distinguish between different energy levels in the semiclassical Bohr model of the atom, The route and movement of an electron within an atom are defined by quantum numbers. Bohr is credited for laying the groundwork for orbital chemistry as we know it today. The principal quantum numbers are represented by the symbol n. The route and movement of an electron within an atom can be described using quantum numbers.The Schrodinger equation must be satisfied when the quantum numbers of all the electrons in a given atom are combined together. Principal, azimuthal or angular momentum, magnetic, and spin quantum numbers are the four forms of quantum numbers. Every number has its own set of properties and value systems.