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

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

Answer: (B)

Verified step by step guidance

1. Recall that the principal quantum number, \( n \), 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 represents discrete energy levels starting from the first shell (\( n = 1 \)) and increasing upwards (\( n = 2, 3, 4, \ldots \)).
3. Recognize that negative integers or zero are not allowed for \( n \) because energy levels cannot be negative or zero in this context; the quantum number must correspond to physically meaningful energy states.
4. Note that \( n \) cannot be any real number because quantum numbers are quantized and only take specific integer values, not continuous values.
5. Therefore, the allowed values for the principal quantum number \( n \) are all positive integers: \( n = 1, 2, 3, \ldots \).