Question

In the photoelectron spectrum of \(\mathrm{Sc}\), the peak at \(0.63 \mathrm{MJ} / \mathrm{mole}\) is assigned to the \(4 s\) subshell. Why is the peak at \(0.77 \mathrm{MJ} / \mathrm{mole}\) in the Sc spectrum assigned as a third subshell of \(n=3\) (named \(3 d\) ) as opposed to being a second subshell of \(n=4\) (that is, \(4 p) ?\)

Short answer

The peak at 0.77 MJ/mole is assigned to a third subshell of \(n=3\) (named 3d) because according to Aufbau principle, 3d orbital is filled before the 4p orbital despite both being in the n=3 shell. This is due to the fact that 3d orbital has a lower energy than 4p orbital.

Step-by-step solution

Understanding Electron Configuration

The first step is to understand that atoms are structured in a way where electrons occupy shells or energy levels surrounding the nucleus. Each shell consists of subshells, which are made up of atomic orbitals. The distribution of electrons among these orbitals is known as electron configuration. Scandium (Sc) has the electron configuration of [Ar] 3d1 4s2.

Interpretation of the photoelectron spectrum

Photoelectron spectroscopy studies the energy required to remove an electron from an atom, which is linked to their initial energy levels. The 0.63 MJ/mole peak corresponds to the 4s orbital which is at a higher energy level than the 3d orbital due to the orbital's increased distance from the nucleus. This gives us the idea that the peak at higher energy on the spectrum corresponds to the electron in an orbital further from the nucleus (higher principal quantum number, n). Hence, the peak at 0.77 MJ/mole must correspond to the electrons in an orbital further from the nucleus than 4s orbitals.

Assignment of 3d and 4p

Now that we understand both electron configuration and photoelectron spectrum, let's see why the 0.77 MJ/mole peak is assigned to a third subshell of n=3 (3d) and not a second subshell of n=4 (4p). According to the Aufbau principle, electrons fill up lower energy levels before moving to higher ones. The 3d orbital fills before the 4p orbital, despite both being in the n=3 shell. Therefore, we can infer that the 0.77 MJ/mole peak which is a relatively lower energy compared to would-be 4p electrons, corresponds to 3d electrons.

Key concepts

Electron Configuration

Electron configuration is essentially the address book for electrons within an atom. It details how the electrons are organized into orbitals, subshells, and shells, which are layers around the nucleus. Considering the address analogy, the shells are like the city, subshells are the streets, and the orbitals are the individual houses where electrons reside.

Now, let's peek into this atomic neighborhood for Scandium (Sc). Sc follows the electron address format of [Ar] 3d1 4s2. This tells us that after filling up the spaces available up to Argon (Ar), Sc adds one electron into the '3d street' and two into the '4s avenue'. This configuration helps explain its behavior in photoelectron spectroscopy, as seen in the solution.

Aufbau Principle

The Aufbau Principle is a fundamental rule in chemistry, acting like a queue system at a busy cafe; electrons will take the first available seat at the lowest available energy level before moving onto higher energy 'seats'.

In this atomic cafe, the 3d orbital is a preferred seating area before the 4p, despite it being in the same ‘n=3 neighborhood’. Think of the 3d orbital as a cozy corner spot that gets filled before the window side 4p tables. This principle guides us through the process of determining electron configuration and is key to understanding the steps in the solution provided.

Atomic Orbitals

Atomic orbitals are like the various rooms within an electron's home, where the probability of finding an electron is highest. Each orbital can house up to two electrons. Scientists have come up with names like s, p, d, and f to describe these rooms' shapes and sizes - with s being round, p dumbbell-shaped, and so on.

These rooms are not all on the same floor; they are spread across different energy levels, akin to different floors in a building. In our example, the '4s' orbital is like an attic space higher up, while the '3d' is a lower floor, but not as accessible until 'the '3s' and '3p' rooms are occupied, as per the steps laid out in the solution.