Explain why the ionisation energies tend to increase across a period

As you go across a period, the next atom will have 1 more proton in its nucleus than the one before. Therefore, the nucleus of each atom will have an increasingly positive charge, meaning a stronger nuclear attraction.

Even though you also have more electrons, all of the electrons are at roughly the same energy level and so there is generally little extra shielding effect or extra distance to lessen the attraction from the nucleus.

In summary, as you go along a period, the outer electrons are more strongly attracted to a more positive nucleus and so it takes more energy to remove it from the outer shell, hence a higher ionisation energy.