We use the periodic table to help us recognize certain trends of physical and chemical properties of the elements. You need to memorize the trends. A trend is generally "it gets bigger" or "it gets smaller" sort of thing. All our trends describe the trend in two directions on the periodic table: 1) across a row, and 2) up and down a column. Here are the important ones for us.
The smallest atom on the periodic table is helium, He, and has a radius of 31 pm. Yeah, He is even smaller than hydrogen, H, which is 53 pm. Which atom is the largest? That would be cesium, Cs, which comes in with a radius of 343 pm. So that is roughly a 10:1 ratio of largest to smallest. Sometimes we just do a generalized bit of rounding as well and say things like atoms range from about 50 pm to 300 pm which is more of a 6:1 ratio. Oh well, you should just wrap your head around the general range of all atomic sizes the extremes are 31 pm and 343 pm... so chopping that to 50-300 pm isn't a big deal.
Atoms get bigger as you go down a column on the periodic table. This is because in going down a column you are jumping up to the next higher main energy level (n) and each energy level is further out from the nucleus - that is, a bigger atomic radius.
Atoms get smaller as you go across a row from left to right. This may seem counterintuitive but it is the fact. The logic is that as you go across rows, you are staying in the same main energy level (n) so electrons are entering the atomic atmosphere at about the same distance. However, as you go across, the nuclei are getting more and more positive (more protons) - therefore there is more + to – attraction and the electron cloud is pulled in tighter and therefore a smaller radius.
So on any one row, the group 1 atoms (alkali metals) are the biggest on that row and the group 18 atoms (noble gases) are the smallest. Below is a simple graphic illustrating the atomic radii trends.
Now that you have the trend for neutral atoms, let's modify or tweak those sizes for when the atom is changed into a cation or anion.
Cations: Metals tend to lose their electrons to make stable cations. The typical number is one to three electrons to make +1, +2, and +3 cations. Realize that when you make a cation from a monatomic neutral species, you are removing electrons from the outmost valence shell. Upon each e– removal, there are fewer e– repulsions which means the remaining electrons are pulled in tighter than before. This means that cations have smaller radii than the neutral atom from which they came from. And, each subsequent removal of additional electrons leads to smaller and smaller cation species. This is illustrated below starting on the left with a neutral atom.
Anions: Non-metals tend to gain electrons to make stable anions. So in a likewise but opposite manner - we ADD electrons to the valence shell thus increasing electron repulsions which means the resulting anion is bigger than the atom from which they came. The more electrons you add, the bigger the anion gets. This is illustrated in the diagram below starting on the left with a neutral atom.
Here's a figure from Wikipedia showing the neutral atomic radii vs the ionic radii sizes for some cations and anions.
Ionization energy is the amount of energy it takes to remove one electron from a neutral atom (A) in order to form a +1 cation. The reaction (with energy shown) is
A + energy → A+ + e–
The energy needed to do this must overcome the attraction of the outermost electron to the nucleus. All atoms have a wide variety of energies needed to do this, but they DO follow a trend that is easily seen on the periodic table. Much like all the trends, the two extremes of this property are at the bottom left (smallest IE) and the top right (largest IE). Going down a column, IE's decrease. Going across rows, IE's increase.
Electron affinity is the amount of energy released when one electron is added to a neutral atom (A) in order to form a –1 anion. The reaction (with energy shown) is
A + e– → A– + energy
You can think of EA as the "desire of an electron" by an atom. If the atom "wants" the electron a lot, then the EA is big. Less desire is smaller energy and there is even no desire and the numbers go to zero and even negative. The trends on the periodic table are not as pronounced as with other trends (they're a bit janky) - but in general, the upper right corner has the largest EAs while the lower left corner has the lowest values. I'm including this for the purpose of pointing out this is a real measurement and the recognition of EA is more important for our studies than the actual values. Move on to electronegativity now.
Electronegativity is a relative scale from zero to four that measures the "desire" or "pull" on electron pairs. Electronegativity is the purposeful human friendly scale from 0 to 4 that electron affinity lacked. The maximum of 4.0 on this scale belongs to fluorine (top right). The minimum of 0.8 on this scale belongs to cesium (bottom left). Think of EN as the "pull" on electron pairs in a molecule by an atom. We use it the most of the three trends/properties last listed. And yes, we ignore the noble gases for EN values because they are happy as is - they have no desire for any shared electrons and they don't form bonds, so no values for them.
We will rarely need the actual numbers for electronegativity. Just knowing approximately which elements are the most electronegative (upper right corner) helps us in recognizing and assigning polarity of bonds and ultimately compounds. The non-metals tend to be at or above 2.0 on the scale which means they "want" electrons far more than all the metals which tend to all be less than 2.0 on the scale. Go to Wikipedia or other online resources if you want the actual numbers for electronegativity.
Below is an illustration showing how the extremes of all properties (trends) are in the same two regions.