The Quantum Model and Electron Configurations: Quick Revision

A brief note on The Quantum Model and Electron Configurations. Read it before a test. Try each question at the end before you open its answer.

Waves and uncertainty

• De Broglie: $\lambda = \dfrac{h}{mv}$.
• Heisenberg: $\Delta x \cdot m\Delta v \geq \dfrac{h}{4\pi}$. No fixed orbit can be known.

Quantum numbers

A subshell has $2l + 1$ orbitals; a shell has $n^2$. Nodes: radial $n - l - 1$, angular $l$.

Filling

• Aufbau: by $(n + l)$, the smaller $n$ first for a tie.
• Pauli: at most two electrons in an orbital, with opposite spins.
• Hund: one electron in each orbital of a subshell before pairing.
• Chromium and copper move one $4s$ electron into $3d$. Ions lose $4s$ first.
• Spin-only moment: $\mu = \sqrt{n(n + 2)}\ \text{BM}$.

A worked example

Manganese is $[\text{Ar}]\,3d^5 4s^2$. Find the configuration and the magnetic moment of $\text{Mn}^{3+}$.

1. Remove three electrons. Two from $4s$, then one from $3d$: $[\text{Ar}]\,3d^4$.
2. Unpaired. Four electrons in five $d$ orbitals, one each: $4$ unpaired.
3. Moment. $\mu = \sqrt{4 \times 6} = 4.90\ \text{BM}$.

Practice with new numbers

A program to try

The program works out the worked example.

Mistakes to avoid

• Taking $3d$ electrons off before $4s$ when forming an ion.
• Letting $l$ equal $n$. It must be smaller.
• Pairing electrons too early. Hund's rule spreads them out first.
• Counting orbitals as electrons. Each orbital holds two.

Check yourself

1. What is the de Broglie wavelength of an electron moving at $1.0 \times 10^{7}\ \text{m s}^{-1}$?

2. How many orbitals are there in a $d$ subshell?

3. Write the configuration of calcium, $Z = 20$.

4. Which principle limits an orbital to two electrons?