Hägg's rule for carbides

Carbon atoms fit into the gaps of a metal lattice if their radius is small enough. You will test four metals with the rule of Hägg: the radius of the guest atom divided by the radius of the host metal must be below 0.59 for a simple interstitial carbide.

The idea. Divide the radius of carbon by the radius of each metal. Compare each ratio with 0.59. Then turn the rule round to find the largest guest atom that a metal can hold.

Your tasks.

1. Fill the dictionary ratio with the radius of carbon divided by the radius of each metal.
2. Set simple to the list of metals whose ratio is below the limit.
3. Set largest to the largest guest radius, in pm, that iron can hold in a simple lattice.
4. Set gap to the radius, in pm, of the octahedral gap in titanium. It is 0.414 times the radius of the host atom.