Finding patterns in the elements

From pictures to numbers

A plot shows a pattern; a number pins it down. In this lesson three tools turn the trends into numbers:

• groupby for the mean of each block or group;
• corr for how closely two columns move together;
• diff for the change from one element to the next.

The mean of each block

Read it in three steps: split the rows by their block, take the ie column of each group, and find its mean. For the first 36 elements the means are about $918.2$ kJ/mol for the s-block, $1124.0$ for the p-block and $722.3$ for the d-block. The p-block is highest because it ends each period with the halogens and noble gases.

agg asks for several answers at once: .agg(["min", "max", "count"]).

Do two columns move together?

The correlation coefficient $r$ is a number from $-1$ to $1$:

• near $1$: when one column is large, so is the other;
• near $-1$: when one is large, the other is small;
• near $0$: no straight-line link.

On this small table it prints $-0.86$. For all 36 elements, the program at the end of this lesson prints $-0.83$. Small atoms hold their electrons tightly, so a small radius goes with a high ionisation enthalpy. Rows with a missing radius are simply left out of the sum.

A correlation is a summary, not a cause. Both columns follow from the same thing: how far the outer electrons are from the nucleus and how well they are shielded.

Finding the breaks

Across period 2 the ionisation enthalpy rises overall, but two elements fall below the one before. diff() finds them. It takes each value minus the value above it, so a fall is negative. Inside each period separately:

The groupby keeps each period apart, so the drop from neon to sodium is not counted. In period 2 the breaks are:

• boron, $98$ kJ/mol below beryllium: its outer electron is in a 2p orbital, higher in energy than the full 2s of beryllium;
• oxygen, $88$ kJ/mol below nitrogen: its fourth 2p electron pairs up, and the repulsion makes it easier to remove. Nitrogen's half-filled 2p is extra stable.

In period 3 the same pattern returns at aluminium and sulphur. In period 4, gallium falls sharply after the full 3d of zinc.

Practise with new numbers

Try it in Python

The program prints the mean ionisation enthalpy of each block and the correlation of radius with ionisation enthalpy, then lists every element that breaks the rise in its period.

Common mistakes

• diff() over the whole table. Without groupby("period"), the fall from a noble gas to the next alkali metal is counted as a break.
• Reading a correlation as a cause. A strong $r$ says that two columns move together, not that one makes the other.
• Forgetting that a fall is negative. diff() gives new minus old, so a break shows as a value below zero.
• Grouping by a misspelt column. df.groupby("Block") stops with KeyError: 'Block'.
• Expecting groupby alone to print numbers. It only splits the rows; add ["ie"].mean() or another sum.

Remember these

• df.groupby("block")["ie"].mean(): split by block, take one column, find the mean of each group.
• df["a"].corr(df["b"]) gives $r$ from $-1$ to $1$; radius and ionisation enthalpy have a strong negative $r$.
• df.groupby("period")["ie"].diff() gives the change from the element before, inside each period.
• The breaks in period 2 are boron and oxygen; in period 3, aluminium and sulphur.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What three steps does df.groupby("block")["ie"].mean() carry out?

2. What does a correlation of $-0.83$ between radius and ionisation enthalpy tell you?

3. Why is diff() grouped by period before looking for breaks?

4. Why does oxygen have a lower first ionisation enthalpy than nitrogen?

5. Which line keeps only the elements that break the rise?