Answer
The atoms or ions with the smallest radii in each set are:
a. Helium (\( \mathrm{He} \))
b. Chlorine (\( \mathrm{Cl} \))
c. Element 116
d. Silicon (\( \mathrm{Si} \))
e. Na$^+$
Work Step by Step
To determine the atom or ion with the smallest radius in each set, we need to consider the periodic trends of atomic radius.
a. \( \mathrm{H}, \mathrm{He} \):
In this set, helium (\( \mathrm{He} \)) has the smallest radius. This is because as we move across a period from left to right on the periodic table, the atomic radius generally decreases. Helium is to the right of hydrogen (\( \mathrm{H} \)) in the periodic table, so it has a smaller atomic radius.
b. \( \mathrm{Cl}, \mathrm{In}, \mathrm{Se} \):
Among chlorine (\( \mathrm{Cl} \)), indium (\( \mathrm{In} \)), and selenium (\( \mathrm{Se} \)), chlorine has the smallest radius. As we move down a group on the periodic table, the atomic radius generally increases. Chlorine is at the top of the group, while indium and selenium are below it. Therefore, chlorine has the smallest atomic radius in this set.
c. element 120, element 119, element 116:
Since the specific elements are not mentioned, it is difficult to determine the exact order of their atomic radii. However, based on the periodic trend, we can assume that element 116 would have the smallest radius. As we move down a group, the atomic radius generally increases. Therefore, element 116, being at the top of the group, would have the smallest atomic radius among these elements.
d. \( \mathrm{Nb}, \mathrm{Zn}, \mathrm{Si} \):
Among niobium (\( \mathrm{Nb} \)), zinc (\( \mathrm{Zn} \)), and silicon (\( \mathrm{Si} \)), silicon has the smallest radius. As we move across a period from left to right, the atomic radius generally decreases. Silicon is to the right of niobium and zinc in the periodic table, so it has a smaller atomic radius.
e. Na$^-$, Na, Na$^+$
Na$^+$ has the fewest electrons as compared to Na$^-$, and Na because it has the smallest number of electron-electron repulsions, which makes it the smallest ion with the largest ionization energy.
