Which of the following best describes the possible values of 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. Understand 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. Recall that \(n\) must be a positive integer because it corresponds to discrete energy levels; it cannot be zero, negative, or fractional.
3. Recognize that the allowed values of \(n\) are \$1, 2, 3, \ldots$, representing the first, second, third, and higher energy levels respectively.
4. Eliminate options that suggest \(n\) can be negative, zero, or any real number, since these do not correspond to physically meaningful energy levels in quantum mechanics.
5. Conclude that the best description is that \(n\) can be any positive integer (1, 2, 3, ...), which aligns with the quantum mechanical model of the atom.