In quantum chemistry, the principal quantum number n primarily indicates which property or properties of an electron in an atom?

Introduction / Context:
Quantum numbers are used to describe the allowed states of electrons in atoms in quantum mechanics. The principal quantum number, symbolised by n, is one of the most important because it is directly related to the main energy levels or shells of an atom. Many exam questions test whether students understand what physical properties are associated with the principal quantum number. This question asks what property or properties of an electron are indicated by the value of n.

Given Data / Assumptions:

• The principal quantum number n can take positive integer values (1, 2, 3, and so on).
• Electrons in higher n levels are generally farther from the nucleus and have higher energy in hydrogen like atoms.
• The options suggest that n might reflect energy, distance, both, or something unrelated such as the total number of subshells in the periodic table.
• We assume a basic understanding of quantum mechanical models of the atom.

Concept / Approach:
The principal quantum number n primarily defines the main energy level or shell that an electron occupies in an atom. In hydrogen like atoms (single electron systems), the energy of an electron depends mainly on n; as n increases, the energy becomes less negative and the electron is less tightly bound. Additionally, the average distance of the electron from the nucleus also increases with n, because higher n levels correspond to orbitals that extend farther from the nucleus. Therefore, n is related both to the energy of the electron and to its average distance from the nucleus. It does not directly specify the total number of subshells in the periodic table, although each shell with principal quantum number n contains n subshells.

Step-by-Step Solution:
Step 1: Recall that the principal quantum number n labels the main energy levels or shells (K, L, M, etc.) of an atom. Step 2: Recognise that as n increases, the energy level of the electron generally increases (becomes less negative), especially for hydrogen like atoms. Step 3: Understand that electrons in higher n shells are, on average, farther from the nucleus, so n also reflects the average distance from the nucleus. Step 4: Compare the options and see that options A and B each cover only one of these aspects, while option C correctly mentions both energy and average distance. Step 5: Recognise that option D, dealing with the number of subshells in the entire periodic table, is not the primary role of the principal quantum number in describing an individual electron.

Verification / Alternative check:
In the Bohr model of the hydrogen atom, the energy of an electron in the nth orbit is given by an expression proportional to 1 / n^2, clearly showing dependence on n. Quantum mechanical treatments also show that the radial distribution of electron probability depends strongly on n, with higher n orbitals having significant probability density farther from the nucleus. These results demonstrate that n is intimately connected with both the energy and the radial size of the electron's region of space. While it is true that each shell with quantum number n possesses n subshells (s, p, d, f, etc.), this is a consequence of the definition, not the primary physical meaning of n for a given electron.

Why Other Options Are Wrong:
Option A states that n indicates only the energy of the electron; this is incomplete because n is also closely related to the electron's average distance from the nucleus. Option B states that n indicates only the distance from the nucleus, again leaving out the important link with energy, especially in hydrogen like systems. Option D focuses on the number of subshells in the periodic table, which is an indirect and less fundamental point, and not the main physical property described by n for an individual electron. Therefore, none of these options fully captures the dual role of the principal quantum number.

Common Pitfalls:
Students sometimes treat quantum numbers as mere labels without connecting them to physical properties such as energy and distance. Another pitfall is to memorise isolated statements like “n gives the shell” without understanding what that implies in terms of electron energy and radial extent. To avoid confusion, remember that higher n means both a higher energy level (in hydrogen like atoms) and an orbital that extends farther from the nucleus on average. Recognising both aspects will help you deal with many quantum number questions more confidently.

Final Answer:
The principal quantum number n primarily indicates both the energy of the electron and its average distance from the nucleus in an atom.