Step-by-step explanation:
An atomic radius is defined to be one-half the distance between the nuclei of two atoms, assuming a spherical atom since, according to the quantum mechanical model of the atom, electrons are located within a probability cloud surrounding the nucleus which has no sharp boundary.
Notice that, in general, there are two main trends of atomic radii in the Periodic Table of Elements.
The first trend illustrates that atomic radii increase when going down a group in the periodic table. This is because when moving downwards in a group, every subsequent atom gains an additional principal energy level, which leads to electron shielding. Electron shielding refers to the decreased attraction between the electrons that occupy the higher principal energy level and the nucleus of the atom due to the shielding of electrons in the lower principal energy level.
The second trend outlines that atomic radii decrease when going across the period from left to right. For elements within a period, individual electrons occupy the same principal energy level. Likewise, when an electron is added, a new proton is also added to the nucleus, providing the nucleus with a stronger positive charge and hence leading to a higher effective nuclear charge. This increase in nuclear attraction pulls the electrons closer towards the nucleus, leading to a decrease in atomic radius.
Therefore, given the option between beryllium, calcium, barium, and strontium, the element with the largest atomic radius is barium since all the elements given are in Group II, however, barium is the element furthest down the group and therefore have electrons occupying the highest principal energy level compared to other elements.