Why does ionisation energy generally increase across a period?

Ionisation energy generally increases across a period due to an increase in nuclear charge without a significant increase in shielding.

In more detail, ionisation energy is the energy required to remove an electron from an atom. As you move across a period in the periodic table from left to right, the number of protons in the nucleus (the nuclear charge) increases. This means that the positively charged nucleus has a stronger pull on the negatively charged electrons, making it harder to remove an electron and thus increasing the ionisation energy.

At the same time, the increase in electrons is balanced by the increase in protons, maintaining the atom's overall electrical neutrality. However, these additional electrons are added to the same energy level, or shell. This means that there is not a significant increase in shielding, or the ability of inner electrons to block the pull of the nucleus on outer electrons.

The combination of increased nuclear charge and minimal increase in shielding results in a stronger attraction between the nucleus and the outer electrons. This stronger attraction means that more energy is required to remove an electron, leading to an increase in ionisation energy across a period.

It's also worth noting that there are some exceptions to this trend. For example, the ionisation energy decreases slightly from beryllium to boron and from nitrogen to oxygen. This is due to the fact that in these cases, the added electron enters a higher energy sub-level or pairs up with another electron in an orbital, which slightly reduces the ionisation energy. However, the overall trend across a period is still an increase in ionisation energy.