To determine the correct answer, we need to examine the roles of quantum numbers in describing an electron's properties within an atom:
1. Principal Quantum Number (n):
- The principal quantum number, denoted as 'n', indicates the energy level of an electron within an atom. It is a positive integer (n = 1, 2, 3, ...).
- Higher values of 'n' correspond to higher energy levels. Therefore, an electron with a higher 'n' (e.g., n = 4) will have more energy compared to an electron with a lower 'n' (e.g., n = 2).
2. Explanation of Options:
- Spin: This is defined by the spin quantum number (ms), which can be +1/2 or -1/2. It is not related directly to the principal quantum number 'n'.
- Stability: Generally, electrons in lower energy levels (smaller 'n') are more tightly bound and thus are more stable. Therefore, it is inversely related to 'n'.
- Energy: Since the principal quantum number directly indicates the energy level, higher 'n' means more energy.
- Wave Nature: All electrons exhibit wave-like behavior as described by quantum mechanics, regardless of their energy levels. This is not influenced by the principal quantum number 'n'.
Given this analysis, we see that the correct property influenced by the principal quantum number is:
c. energy
Thus, the electron with [tex]\( n = 4 \)[/tex] has more energy than the electron with [tex]\( n = 2 \)[/tex].
