In a neutral atom, how many principal energy levels (shells) are possible according to the quantum mechanical model?

• A. There is no theoretical limit; energy levels are numbered n = 1, 2, 3, ...
• B. Only 3 energy levels exist in any atom.
• C. There are exactly 7 energy levels for all atoms.
• D. Atoms have a maximum of 4 energy levels.

Answer: (A)

Verified step by step guidance

1. Understand that in the quantum mechanical model of the atom, principal energy levels (or shells) are designated by the quantum number \(n\), where \(n = 1, 2, 3, \ldots\).
2. Recognize that each principal energy level corresponds to a shell that can hold electrons with increasing energy as \(n\) increases.
3. Recall that theoretically, there is no upper limit to the value of \(n\); energy levels can continue to increase indefinitely, although higher levels are less stable and less commonly occupied in neutral atoms.
4. Note that while atoms commonly have electrons in the first few shells (like \(n=1\) to \(n=7\)), this is due to practical electron configurations and not a strict theoretical limit.
5. Conclude that the quantum mechanical model allows for an infinite number of principal energy levels, so the correct understanding is that there is no theoretical limit to \(n\).