Final answer:
The radius of the valence shell of Na is larger than the radius of the valence shell of Li. This is because sodium is located below lithium in the periodic table, meaning it has a higher principal quantum number and more electron shells, thus a larger atomic and valence shell radius.
Step-by-step explanation:
The student has asked whether the radius of the valence shell of Na is larger, smaller, or the same compared to the radius of the valence shell of Li. The answer is larger. This is because, according to the periodic trend, as we move down a group in the periodic table, the principal quantum number, n, increases. Thus, for each element that comes after in the group, an additional electron shell is added, increasing the atomic radius. Both sodium (Na) and lithium (Li) are in the same group with sodium being the lower of the two, thus having more electron shells compared to lithium and a larger radius for its valence shell.
When comparing ion sizes, we must account for effective nuclear charge and electron-electron repulsions. For cations, the loss of electrons results in a decrease in electron-electron repulsion and an increase in the effective nuclear charge experienced by the remaining electrons, which makes cations smaller than their neutral atoms. Conversely, anions, which gain electrons, have increased electron-electron repulsion and a reduced effective nuclear charge on the added electrons, thus making anions larger than their neutral atoms.
Therefore, since Na and Li are both alkali metals and lose one electron to form cations, the sodium cation (Na+) would have a valence shell with n = 2, while lithium (Li+) would have a valence shell with n = 1. Coupled with a larger effective nuclear charge and reduced electron-electron repulsion, sodium has a larger atomic radius than lithium, and this extends to their valence shells as well.