Which quantum number must be the same for the electrons in the three orbitals shown below? 17A

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The question presents three orbitals and asks which quantum number must be the same among the electrons occupying them.
Option 1: Magnetic spin quantum number, ms. While electrons can have the same ms when paired, there is no requirement that ms be identical for electrons in different orbitals; ms can be +1/2 or -1/2 and may vary between electrons. Therefore, this option isn’t a universal necessity across the three orbitals.
Option 2: Angular momentum quantum number, l. If the three orbitals are drawn from the same subshell, they share the same l (the same angular momentum). This is a key constraint: electrons in the same subshell have the same l value but may differ in ml and ms. Given typical diagrams of three orbitals that appear to be of the same subshell, l being common is a solid requirement.
Option 3: All 3 must be different. There is no general rule that all three orbitals must have different quantum numbers; in particular, they can share the same l and still be distinguished by ml values. Thus this statement is incorrect as a universal rule.
Option 4: Magnetic quantum number, ml. In many orbital illustrations, the three orbitals differ by ml (for example, ml = -1, 0, +1 in a p-sublevel), so they are not all forced to share ml. The question asks what must be the same, not what can vary, so this option is not a universal truth.
Option 5: None of the 3 must be different. This would imply there is no requirement for any of the quantum numbers to be the same, which contradicts the common scenario where electrons in the same subshell share l. Since l is often fixed across those orbitals, this statement is inaccurate as a general rule.

Which quantum number must be the same for the electrons in the three orbitals shown below? 17A

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