As astrophysicist Neil deGrasse Tyson is fond of saying, "Humans are pattern-seekers." We try to figure out patterns in seemingly random places; sometimes those patterns are real, but sometimes they lead us astray.
We have already seen the basic structure of the Periodic Table, and have drawn Bohr-Rutherford diagrams to show how electrons are arranged. Extending that, we can use patterns in the Table to predict how elements will behave -- and Mendeleev himself knew this when he was coming up with his initial version.
There is an excellent video which shows how different alkali metals (Group 1) behave when they are placed in water.
With a little freeze-frame wizardry, we can compare these reactions side-by-side to see if there is a trend as you go down Group 1.
Based on this evidence, you can come to this conclusion:
As you go down Group 1, the elements get more reactive.
On the other side of the Periodic Table, in Group 17, are the halogens. They are all very reactive elements, but the trend is different.
Here is a sample of steel wool (called "iron wool" in the UK). You can buy it in any hardware store, and it is used to polish things like metal. (Don't use it to clean delicate metal objects, though, as it will remove a thin layer of that metal.)
Here is a summary of how steel/iron wool reacts with four halogen elements.
Fluorine, at the top of Group 17, reacts violently. Iodine, at the bottom, reacts very slowly. (Don't worry about the (III) in the middle of the chemical name for now.)
Based on this evidence, you can come to this conclusion:
As you go down Group 17, the elements get less reactive.
We can summarize both of these together in a diagram:
In a sphere, the radius is the distance from the centre out to the edge, in any direction.
We can think of atoms as being like tiny spheres, with the nucleus in the middle. If we look at the radius of a neutral atom of a variety of different elements, we can see the trend. These distances are given in picometres (pm), which is a millionth of a millionth of a metre... so, pretty small.
Pick one period or group and look at the numbers. No matter what period or group you choose, it always follows the same pattern.
A couple of small things to note here:
Groups 3 through 12 are left out here, as they follow their own rules and there can be some strange things happening with those elements.
This diagram uses the old convention of naming groups, using "A" and "B" for different group numbers. Please just use the newer, better, 1-18 convention.
Based on the information above, we can come to these two conclusions:
As you go down in the same group, atomic radius increases.
As you go from left-to-right in the same period, atomic radius decreases.
There are many more patterns in the Periodic Table; these are just a few. Mendeleev used these patterns to predict the physical and chemical properties of elements that hadn't yet been discovered by the 1860s: he left blank spaces, knowing they would later be filled-in by someone else.
Compare the reactivity of (a.) lithium and cesium, and (b.) fluorine and iodine.
Which has a larger atomic radius, magnesium or sulphur?
Which has a larger atomic radius, nitrogen or antimony?
Look up the melting points of all the alkali metals on a website such as Ptable. Do you see the trend?