Building the Periodic Table — Question 4

Question 4

Chromium and copper expose the limits of a simple filling order

The empirical neutral ground configurations are $\mathrm{Cr}:[\mathrm{Ar}]3d^54s^1$ and $\mathrm{Cu}:[\mathrm{Ar}]3d^{10}4s^1$. Their atomic numbers are 24 and 29. A simple filling mnemonic would instead give $3d^44s^2$ and $3d^94s^2$.

1. Check the electron counts and determine whether the mnemonic configurations violate exclusion.

2. Using Hund spin alignment for the supplied ground configurations, find S for Cr and Cu.

Question 4 - Solution

Chromium and copper expose the limits of a simple filling order

(a) Method and calculation

$$N_{\mathrm{Cr}}=18+5+1=\boxed{24},\quad N_{\mathrm{Cu}}=18+10+1=\boxed{29}.$$$$d^4s^2:\ 4\le10,\ 2\le2;\quad d^9s^2:\ 9\le10\Rightarrow\boxed{\text{both Pauli allowed}}.$$

(b) Interpretation and further calculation

$$\mathrm{Cr}:\quad S=5(1/2)+1/2=\boxed{3}.$$$$\mathrm{Cu}:\quad S_d=0,\quad S_s=1/2\Rightarrow\boxed{S=1/2}.$$

Physical check

The empirical configurations reflect total atomic energy, including interactions. Exclusion permits both candidate patterns and cannot by itself decide which is lower.