for an ionization energy vs. atomic number graph it is a relatively jagged graph as you go across a period. Why does this occur?

Mostly because the added electrons are going into different sub-levels; i.e., s, p, d, f, etc.

oh okay thanks.

This stuff kind of confuses me. The ionization energy and stuff, i don't really get how it all works

For example, let's take Na, Mg, Al.

Na = 11 electrons; 1s2 2s2 2p6 3s1 so the outside electron "sees" 1 + charge (the 11 protons in the nucleus are shielded by the 10 1s2 2s2 2p6 electrons). So the ionization energy is essentially 1e versus 1+.

Mg is 1s2 2s2 2p6 3s2.
We have 12 + charges in the nucleus, the outside electron is pulled by a +2 charge (nucleus is +12-10 electron shielding = 2+ charge) so it is harder to pull the first electron away from Ng than from Na.

Al is 1s2 2s2 2p6 3s2 3p1.
Note here that the added electron is now in the 3p (Na and Mg didn't have that) so we have 13+ in the nucleus and the outside 3p1 electron is shielded by 12 electrons so we shouldn't expect to have as much energy to pull the 3p1 electron away from Al as it took for the Mg (and it doesn't). The energy for Na is about 5.1, for Mg about 7.4 and for Al about 6. That's the jagged edge the question refers to.

The relatively jagged graph of ionization energy vs. atomic number across a period can be attributed to several factors. To understand why this occurs, we need to consider the underlying principles of atomic structure and the trends in ionization energy.

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. It depends on factors such as the atomic radius, nuclear charge, and electron configuration.

1. Atomic Radius: As you move across a period from left to right, the number of protons in the nucleus increases, resulting in a greater positive charge. This increased positive charge attracts the electrons more strongly, decreasing the atomic radius. With a smaller atomic radius, electrons are held more tightly, requiring more energy to remove them, leading to a higher ionization energy.

2. Effective Nuclear Charge: Along with the increase in protons across a period, there is also an increase in the number of electrons. This creates a phenomenon called shielding, where inner electrons partially shield the outer electrons from the full effect of the positively charged nucleus. However, the increase in effective nuclear charge, which is the net positive charge experienced by the outer electrons, offsets this shielding effect. As a result, the electrons are more strongly attracted to the nucleus, leading to higher ionization energy.

3. Electron Configuration: The electron configuration of an atom describes how its electrons are distributed within different energy levels or orbitals. When moving across a period, the electrons are added to the same energy level (principal quantum number), resulting in a similar shielding effect. However, the addition of electrons to the same energy level does not significantly increase the shielding effect, but instead increases the repulsive forces between electrons. This increased repulsion makes it easier to remove an outer electron, resulting in a decrease in ionization energy compared to the previous element.

In summary, the jagged graph of ionization energy vs. atomic number across a period occurs due to the interplay of multiple factors: the increasing effective nuclear charge, decreasing atomic radius, and the electron configuration. It is the combined effect of these factors that results in variations in ionization energy as you move across a period.