Although it may seem counterintuitive, atomic radius does decrease from left to right on the periodic table. The reason for this is because the added positive charge in the nucleus causes the elctrons to be pulled more strongly towards the center, which decreases the atomic radius.

Electronegativity values become greater as you move up and to the right on the periodic table. Of the four atoms listed, sulfur is the highest up and farthest to the right, giving it the greatest electronegativity.

Ionization energy is the amount of energy that an atom in the ground state must absorb to emit an electron. Upon ionization, a cation is formed. Ionization energy increases from bottom to top within a group, and from left to right within a row of the periodic table which is the opposite trend that atomic radius follows. Referring to the periodic table, we can see that of these group VII elements, fluorine has the highest ionization energy.

All of these atoms are in group VII. Within a group, atomic radii increase from top to bottom due to the increased number of electron shells.

Ionization energy is the amount of energy that an atom in the ground state must absorb to emit an electron. Upon ionization, a cation is formed. Ionization energy increases from bottom to top within a group and from left to right across a period in the periodic table which is the opposite trend that atomic radius follows. Referring to the periodic table, it can be seen that helium has the highest ionization energy of those in the list. 

There are four main periodic trends: electronegativity, atomic size, ionization energy, and electron affinity. Electronegativity measures how easily an atom can attract an electron to form a covalent bond, atomic size (as the name implies) measures the size of the atom, ionization energy measures the amount of energy required to remove an electron, and electron affinity measure the amount of energy released upon absorption of an electron. Electronegativity increases as we go towards the top right of the periodic table (Fluorine has the highest electronegativity), atomic size increases as we go towards the bottom left, ionization energy increases as we go towards top right, and electron affinity increases as we go towards top right.

This means that as we go left to right, electronegativity, ionization energy and electron affinity will increase.

To answer this question, we need to look at the electronegativity periodic trend. Recall that electronegativity increases as you go towards the top and right of the periodic table. For example, fluorine (the most top-right, non-noble gas element on the periodic table) has the highest electronegativity (note that noble gases have no reactivity, so electronegativity is not measured for them).

The question states that  in molecule B is at the top right. This means that  has the higher electronegativity. The polarity of a molecule is calculated using the electronegativity differences between the atoms in the molecule. The higher the electronegativity difference, the more polar. Since  in molecule B has the higher electronegativity, molecule B will be more polar (larger electronegativity difference) than molecule A.

Recall that like dissolves like. Water is a highly polar molecule; therefore, polar molecules will dissolve more easily in water (in our case, molecule B). To traverse the hydrophobic interior of a cell membrane, a molecule should be nonpolar; therefore, molecule A will have an easier time traversing the membrane.

Electron affinity is the energy released when an atom gains an electron. The amount of energy released is higher if the atom readily accepts the electron and has high affinity, or ‘attraction’, for the electron. As we go towards the right on the periodic table, elements like to gain electrons to complete their octet; therefore, electron affinity increases as we go towards the right. As we go down, electron affinity decreases because of increases in atomic size. This means that the electron affinity increases as we go top-right. The only other listed periodic trend that increases as we go top-right is electronegativity.

Note that number of valence electrons and polarity are generally not considered periodic trends.

Ionization energy is the energy required to remove an electron. Ionization energy decreases as we go towards the bottom-left on the periodic table. As we go left on periodic table the ionization energy decreases because electrons in the outermost shell are readily willing to give up their electrons to complete the octet. For example, lithium has one valence electron in its outermost shell (). The lithium atom will readily give up its one valence electron to complete its octet (or doublet in the case of lithium because the innermost shell only contains two electrons). Note that the ionization energy to remove innermost electrons of lithium is extremely high. This occurs because it takes a lot of energy to destabilize the octet.

The ionization energy decreases as we go towards the bottom of the periodic table because the atomic size increases, making it easier to remove the electron.

Negative ions contain larger radii than their atom counterparts. When an atom becomes an anion, the valence shell becomes crowded with electrons. This results in an increase in repulsive forces, thereby increasing the atomic radius. 

Conversely, positive ions contain smaller radii than their atomic counterparts. When a cation is formed, the protons in the nucleus outnumber the electrons surrounding the atom. This results in a stronger pull towards the nucleus, which in turns reduces the atomic radius. Also, recall that it is the valence electrons that are removed in cations, thus the cationic form may have a lower principal quantum number.