Within a row, atomic radius increases as elements go from right to left on the periodic table. There are more proton in the rightmost elements which pulls the electrons closer into the nucleus due to their opposite (attractive) charges. Atomic radius increases from top to bottom within a group because new energy shells are added, which makes the radius larger by definition.

Electronegativity increases as the we move up and to the right of the periodic table. Noble gases are stable by themselves and have very low electronegativities. Fluorine is the most electronegative, because it is the most upper right element that is not a noble gas.

Electrons have a negative charge. Protons have a positive charge. Through Coulombic interactions, they are attracted to each other. Increasing the charge increases the attraction between them, and thus increases their pull on each other. Also, going from left to right of the periodic table does not indicate any additional energy shells, so each added electron is the same distance from the nucleus, as opposed to going from the top to the bottom of the periodic table, where new energy levels are added and subsequent elements have electrons that are further from the nucleus, thus greatly increasing the atomic radius.

The atomic radius of atoms will decrease across a period from left to right. Atomic radius is defined by two factors. The amount of electron shells in the atom, and the attraction between the protons in the nucleus and the electrons. Going across the period atoms will have more protons and electrons. This increases the amount of attraction between them and creates a higher nuclear charge. Since the attraction is stronger, the distance between the electrons and protons will be shorter. This means that that the atomic radius is smaller. 

Electronegativity is the likelihood of an element to attract electrons and from bonds. Generally speaking all atoms follow the octet rule. They want to have eight electrons in the outer electron shell. Across a period there are more electrons in the outer shell. The elements are closer to achieving the octet rule, and thus they are more reactive. 

First ionization energy is the amount of energy required to remove an electron from an atom. Elements on the left side of the periodic table have less electrons in their outer shell. This means they will achieve the octet rule more easily by giving away their electrons, and are more likely to do so. Elements on the right side of the periodic table have more electrons in their outer shell, and will have an easier time achieving the octet rule by gaining electrons.

The atomic radius from sulfur to argon decreases. The amount of protons and electrons increases from sulfur to argon. With more protons and electrons the attraction is stronger. This draws the nucleus and outer electron closer together, and the atomic radius is smaller. Potassium however puts the latest electron into a new electron shell. Even though potassium has one more electron and one more proton than argon, the extra electron shell will increase the atomic radius. 

The amount of electrons in the outer shell is easily determined by which group an element is in. Elements in group 15 have 5 electrons in the outer shell. P is the only listed element in group 15.

Lithium has the greatest ionization energy because it is the smallest of the options available. The smaller an element/atom is, the closer to the nucleus of the atom the valence electrons are. The closer valence electrons are to the center of an atom, the harder it us to take one away, because it's strongly attracted to the protons in the center of an atom. The trend for ionization energy is as follows: ionization energy increases from left to right within a row and from bottom to top within a group on the periodic table.

Lithium has the greatest ionization energy because it is the smallest of the options available. The smaller an element/atom is, the closer to the nucleus of the atom the valence electrons are. The closer valence electrons are to the center of an atom, the harder it us to take one away, because it's strongly attracted to the protons in the center of an atom. The trend for ionization energy is as follows: ionization energy increases from left to right within a row and from bottom to top within a group on the periodic table.