Why does nuclear radius decrease and first ionisation energy increase across the period?

As we move across the period electrons occupy the same outer electron shell, having roughly the same distance to the nucleus. Moving across the period nuclear charge increases as the number of protons in the nucleus increases, conversly nuclear shielding remains about the same across the row meaning the effective nuclear attraction rises and therefore the nuclear radius also reduces. Because the attraction betweent outer electrons and the nuclear is higher, more energy is required to ionise the atom (remove an electron).