← Multielectron Atoms and Molecules

# Outer Electrons, Screening and Optical Transitions

Wednesday, March 16, 2022

## Ionization Energy of Outer Electrons

Elements in the first group of the periodic table are called alkali elements, and they all have one outer electron. For instance, lithium ($1s^2~2s^1$). These elements are highly reactive since they give up their outer electron very easily.

To think about the lithium atom, imagine the nucleus and two inner electrons as one shell. We expect the $2s$ electron to be found farther from the nucleus than the $1s$ electrons on average, and we can predict the electrostatic force the outer electron experiences as a result of the $1s$ shell and nucleus using Gauss's Law.

Since the inner electrons are almost certainly found within a sphere centered at the nucleus, their net charge can be thought of as a point charge at the center of the atom. Therefore, the net charge is the nucleus ($+3e$) and two electrons ($-2e$) for a total charge of $+e$.

Using the equation for the energy required to remove an electron given its principle quantum number, $n$, and effective atomic number (charge of the inside sphere), we see that the ionization energy of lithium is actually quite small:

$E_n=\left(-13.60~\text{eV}\right)\frac{Z_{\text{eff}}^2}{n^2}=-3.40\text{eV}$

And while this is not exactly the ionization energy measured ($5.39\text{eV}$), it is close.

## Electron Screening

Consider the excited state of lithium (where an electron goes into the $2p$ suborbital). In this case, the ionization energy is about $3.54\text{eV}$, almost exactly the predicted value. This suggests that in the ground state, something else is going on.

The effect, known as electron screening, is when the charge of the nucleus is screened or shielded by the inner electrons. For non-penetrating orbits (such as the excited lithium atom), the nucleus and inner electrons behave effectively as a hydrogen nucleus. However, this only works for electrons in orbits where the electron is not likely to be found close to the nucleus.

## Optical Transitions

The outer electrons of atoms can be excited (or removed), allowing other electrons to fill the place of the removed electron. When this happens, the energy lost by that electron is often emitted as a photon (called an optical transition when the photon is in the visible range).

The binding energies of outer electrons is often very little (on the order of several electron-volts), meaning it takes very little energy to produce an optical transition.

The wavelengths of the photons emitted relate directly to the energy levels of the outer electrons excited to produce the optical transition. Inner electrons can be ignored in participating.

### Fluorescence

Under "black lights" (sources of ultraviolet radiation), some materials' electrons absorb the energy and emit photons in the visible range. These photons often have wavelengths in the blue/violet region of the visible spectrum, unlike their appearance under sunlight.

This makes sense because the sun emits light primarily in the center of the visible spectrum (yellow) and very little on the ends (red, blue, violet). This means photons from the sun do not have enough energy to excite outer electrons to levels where they would emit blue light. However, ultraviolet light does have enough energy where blue and violet photons are emitted.