Why does the observed pattern for first ionization energy within a period occurs?

Over a period of time, the general trend for (first) ionization energy is an increase from left to right.

Why does this occur?

As you proceed from left to right, you will encounter elements that have one extra proton and one extra electron in their atoms. Consequently, the electric force between protons and electrons increases, causing the electrons to be "pulled" in closer to the nucleus and shrinking in size.

It can be observed that nonmetals, on the right side of the table with more outer electrons, tend to gain electrons to form anions, while metals, on the left side with fewer valence electrons, tend to lose electrons to form cations.

The ionization energy of the atom causes this general tendency of "gaining" an electron rather than "losing" one (or vice versa); metals (left side) have fewer electrons in the outer shell, so removing them will be easier (lower ionization energy), and nonmetals (right side) have larger concentrations of charged particles in more densely packed areas and are smaller. Fulfilling an octet is easier when gaining electrons, so removing electrons from nonmetals is not very energetically favorable.

Taking all of this into consideration, it clarifies why an atom's ionization energy rises from left (for metals) to right (for nonmetals).

The observed pattern for first ionization energy within a period is due to increasing effective nuclear charge, leading to stronger attraction between electrons and the nucleus. As electrons are added to the same energy level, the shielding effect remains constant, resulting in a stronger pull on electrons and higher ionization energy across the period.