Why does the first ionisation energy of atoms generally increase across a period?

The first ionisation energy is defined as the energy required to remove one mole of electrons from each atom of a mole of gaseous atoms. As we go along a period in the periodic table, the atomic number increases. As the atomic number increases, the number of protons in the nucleus increases. This causes the electrostatic attraction between the nucleus and the outermost electron to generally become stronger across a period.