Plotting periodic trends

Why plot?

A column of 36 numbers hides its pattern. A plot shows it at once: the ionisation enthalpy climbs across each period and falls sharply at the start of the next. This is the periodicity that the periodic law describes.

The first plot

matplotlib draws the plot. Two calls do most of the work:

"o-" draws a dot at each element and joins them with a line. Every axis gets a label with its unit; a plot without units is only half an answer.

Reading the plot

• Peaks come at the noble gases, He, Ne and Ar, and at the end of each period. A full shell holds its electrons tightly.
• The deepest troughs come just after them, at Li, Na and K. Each starts a new shell, and its one outer electron is far from the nucleus and well shielded.
• Across a period the values rise overall, because the nuclear charge grows while the shell stays the same.
• The d-block stretch, from Z $= 21$ to $30$, is low and nearly flat, because the added electrons go to an inner shell.

Colour by block

A scatter plot can give each point its own colour. A dictionary turns the block letter into a colour, and map applies it to the whole column:

Now the s-block troughs, the p-block climbs and the flat d-block are easy to tell apart.

Labels on chosen points

annotate writes text beside a point. A filter picks the points to label, and a loop writes them:

iterrows() gives each row in turn; the _ takes the row number, which is not needed here.

Radius: across and down

The second trend is the atomic radius. Across period 3, from sodium to chlorine, it falls from $186$ pm to $99$ pm. Down group 1, from lithium to potassium, it rises from $152$ pm to $231$ pm. Two lines on one set of axes, each with a label, and plt.legend() names them.

Two plots in one figure

plt.subplots(2, 1) makes a figure with two plots, one above the other. Each is an axes object, and you draw on it with ax.plot, ax.scatter and ax.set_ylabel, the same names as before with ax. in front.

Practise with new numbers

Try it in Python

The program draws the ionisation enthalpy of the first 36 elements, coloured by block with the noble gases labelled, and below it the radius across period 3 and down group 1.

Common mistakes

• No units on the axes. Write them in the label: "Atomic radius (pm)".
• A colour for a block that is missing from the dictionary. map gives NaN for it, and the point is drawn without a proper colour. Every block letter needs a key.
• Joining the radius points across a gap. The noble gases have no radius here. Filter them out with df["radius"].notna() before you plot, or the line breaks oddly.
• Forgetting plt.show(). In some places the plot is never drawn without it.
• Mixing plt. and ax. calls on a figure with two plots. Draw on the axes you mean: ax1.plot, ax2.plot.

Remember these

• plt.plot(x, y, "o-") draws points joined by a line; plt.scatter(x, y, c=colours) gives each point a colour.
• df["block"].map(colours) turns block letters into colours, for every row.
• Label every axis with its quantity and unit, and name each line with label and plt.legend().
• Ionisation enthalpy peaks at the noble gases and dips at the alkali metals; radius falls across a period and rises down a group.

Check yourself

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

1. On a plot of ionisation enthalpy against Z, what comes just after each peak, and why?

2. What does df["block"].map(colours) give for a row whose block is "f", if colours has only s, p and d?

3. Why does the radius fall across period 3 but rise down group 1?

4. Which call makes one figure with two plots side by side?

5. Why should the noble gases be left out before plotting the radius?