Which of the following best explains this difference in reactivity?
a. the electron affinity of sodium is smaller than that of cesium.
b. the effective nuclear charge for cesium is less than that of sodium.
c. the first ionization energy of cesium is less than that of sodium.
d. sodium has greater metallic character than does cesium.
e. the atomic radius of cesium is smaller than that of sodium.

The correct option is: c. The first ionization energy of cesium is less than that of sodium

Explanation:

In the periodic table of chemical elements, the alkali metal group is the group 1 of the table which belongs to the s-block.

When going down the group, the atomic number and thus the atomic radius increases. Therefore, the effective nuclear charge decreases and the ionization energy i.e. the energy required to remove the valence electron from gaseous atom, also decreases down the group.

Thus we can say that the metallic character, i.e. the tendency to lose valence electron, increases down the group.

As the effective nuclear charge decreases, therefore, the electronegativity i.e. tendency of an atom to attract the bonded electrons, and electron affinity also decreases down the group.

As the ionization energy, electronegativity, electron affinity decreases and the metallic character increases down the group. Therefore, the reactivity of an alkali metal also increases down the group.

Since, sodium belongs to group 1 and period 3 and cesium belongs to the group 1 and period 6 of the periodic table.

Therefore, ionization energy, electronegativity, electron affinity of cesium is less than sodium.

As the ionization energy of cesium is less than sodium. Therefore, the metallic character and thus the reactivity of cesium is more than sodium.

nacl is added to the aqueous of what? ? in order to get a proper answer you have to specify the exact composition of the aqueous solution.