Which of the following best describes the allowed values for the principal quantum number n in an atom?

• A. n can be any positive integer (1, 2, 3, ...)
• B. n can be any real number
• C. n can be any integer, positive or negative
• D. n can be any nonzero integer

Answer: (A)

Verified step by step guidance

1. Recall that the principal quantum number, denoted as \(n\), is a quantum number that determines the main energy level or shell of an electron in an atom.
2. Understand that \(n\) must be a positive integer because it corresponds to discrete energy levels where electrons can exist; these levels start from 1 and go upwards (1, 2, 3, ...).
3. Recognize that \(n\) cannot be zero or negative because such values do not correspond to physically meaningful energy levels in the quantum mechanical model of the atom.
4. Note that \(n\) cannot be any real number because energy levels are quantized, meaning electrons can only occupy specific, discrete energy states, not continuous values.
5. Therefore, the allowed values for the principal quantum number \(n\) are all positive integers: \(n = 1, 2, 3, \ldots\).