Testing the shielding rule

You will test the model of the contraction against the measured radii. A function gives the effective charge after a number of steps from lanthanum. Another gives the model radius, and a third finds the worst error. The last scans the shielding constant $s$ to find the value that fits best.

The idea. $Z_{eff} = 11.25 + (1 - s) \times i$ after $i$ steps. The model radius is $103.2 \times 11.25 / Z_{eff}$ in pm. The best $s$ is the one with the smallest worst error.

Your tasks.

1. Complete z_eff(i, s).
2. Complete model_radius(i, s).
3. Complete worst_error(s) so that it returns the largest difference, in pm, between the model and the measured radii over all 15 ions.
4. Complete best_shielding() so that it tries s from 0.70 to 1.00 in steps of 0.01 and returns the one with the smallest worst error.