The atomic orbital for an electron in an atom with the quantum numbers n = 4, l = 3, ml = 0, ms = –
1

2
is

Question

The atomic orbital for an electron in an atom with the quantum numbers n = 4, l = 3, ml = 0, ms = –
1

2
 is

BlackTom AI · Accepted Answer

To identify the orbital, we start by linking the given quantum numbers to orbital types.

Option 3d: This would require l = 2, since d orbitals correspond to l = 2. Here l = 3, so a 3d designation is inconsistent with the given l value.

Option 4f: The letter f corresponds to l = 3. Since n = 4 and l = 3, the principal and azimuthal quantum numbers align with a 4f orbital. The subshell notation 4f is appropriate because the principal quantum number tells us the shell (n = 4), and the azimuthal quantum number (l = 3) tells us the subshell type (f).

Option 4s: The s subshell has l = 0. With l = 3, an s designation cannot occur for these quantum numbers, so 4s is not possible.

Option 4p: The p subshell has l = 1. Since l = 3 here, a p designation would be incorrect for this set of quantum numbers, ruling out 4p.

Option 4d: The d subshell corresponds to l = 2. Given l = 3, a d designation would not match; thus 4d is not compatible with the provided quantum numbers.

Overall, the only option that matches both n = 4 and l = 3 is a 4f orbital, because the combination n = 4 defines the shell and l = 3 defines the f subshell. The magnetic quantum number ml = 0 is allowed within the f set (ranging from -3 to +3), and the spin projection ms = -1/2 describes the electron's spin, which does not change the subshell designation, only the spin state of the electron within that orbital.

The atomic orbital for an electron in an atom with the quantum numbers n = 4, l = 3, ml = 0, ms = – 1 2 is

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