Question

select the correct location on the image. the orbital diagram shows the valence electrons of sulfur, which has 16 electrons. if the electrons were added to the atom one at a time, which would be the last electron to occupy an orbital? the orbital diagram includes a 3s orbital with paired electrons (↑↓) and a 3p subshell with three orbitals: the first 3p orbital has paired electrons (↑↓), the second and third 3p orbitals have single electrons (↑ each).

Explanation:

To determine the last electron's orbital in sulfur (atomic number 16), we follow the Aufbau principle, Pauli exclusion principle, and Hund's rule.

Step 1: Electron Configuration of Sulfur

Sulfur has an atomic number of 16, so its electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^4\). The valence electrons are in the \(3s\) and \(3p\) orbitals.

Step 2: Filling Order of Orbitals

• The \(3s\) orbital can hold a maximum of 2 electrons (Pauli exclusion principle: opposite spins). It is filled first with 2 electrons (paired).
• Next, the \(3p\) orbitals (there are 3 \(3p\) orbitals: \(3p_x\), \(3p_y\), \(3p_z\)) are filled. According to Hund's rule, electrons fill degenerate (same energy) orbitals singly with parallel spins before pairing up.
• The \(3p\) subshell has 4 electrons. The first 3 electrons fill each of the 3 \(3p\) orbitals singly (with parallel spins), and the 4th electron pairs up with one of the singly - occupied \(3p\) orbitals.

Step 3: Identifying the Last Electron

We start filling electrons one by one:

1. Fill \(3s\) with 2 electrons (paired).
2. Fill the three \(3p\) orbitals with 1 electron each (total of 3 electrons in \(3p\) at this stage, all unpaired).
3. The 16th electron (last electron) will pair up with one of the already singly - occupied \(3p\) orbitals. Looking at the given orbital diagram, the \(3p\) orbitals have one orbital that is still unpaired (the one with only one electron) before the last electron is added. The last electron will go into the \(3p\) orbital that currently has one electron (to pair with it). In the diagram, among the three \(3p\) orbitals, two have one electron (unpaired) and one is paired? Wait, no, the diagram shows \(3s\) with two electrons (paired), and \(3p\) with one paired and two unpaired? Wait, no, the \(3p\) orbitals in the diagram: let's count the electrons. \(3s\) has 2, \(3p\) has \(2 + 1+ 1=4\) (since sulfur has 6 valence electrons? Wait, no, sulfur has atomic number 16, so electron configuration is \(1s^22s^22p^63s^23p^4\), so valence electrons are \(3s^23p^4\) (total 6 valence electrons). Wait, the diagram shows \(3s\) with 2 (paired), and \(3p\) with \(2 + 1+ 1 = 4\)? Wait, no, the \(3p\) orbitals: the first box has two electrons (paired), the second and third have one each (unpaired). So the electrons in \(3p\) are \(2 + 1+ 1=4\), and \(3s\) has 2, total valence electrons \(2 + 4=6\), which matches (\(3s^23p^4\)).

Now, when adding electrons one by one, after filling \(3s\) (2 electrons), we fill the \(3p\) orbitals. The first three electrons in \(3p\) go into each of the three \(3p\) orbitals (one each, unpaired). The fourth electron (the last one, since \(3s\) has 2 and \(3p\) needs 4 for sulfur's valence) will pair with one of the already singly - occupied \(3p\) orbitals. So the last electron will occupy the \(3p\) orbital that currently has one electron (the second or third \(3p\) orbital in the diagram, the ones with a single electron) to pair with it.

Answer:

The last electron will occupy the third (the right - most) \(3p\) orbital (the one with a single electron) to pair with the electron already present there. In the given diagram, it is the right - most box in the \(3p\) orbital set.