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Caesium has the largest atomic radius because it has the furthest distance electron shell filled, while having the smallest overall nuclear charge. In other words, it has a larger atomic radius than the elements above it in the periodic table because they don't have as many electron shells filled -- the electron shells that fill last are further away from the nucleus. The reason it has a larger atomic radius than the elements to the right of it is because it has a less overall nuclear charge (fewer protons), so it pulls on the electrons in the outer shell less than the others. The reason it has a larger atomic radius than Francium is because, well, we don't know whether it does. But since Francium is extremely unstable, we're unsure. It may be smaller because of other various effects which can be difficult to comprehend.
the alkali metals have the largest radius per mass because they have the electronic configuration of the noble gasses plus one electron, this last electron must go into a new atomic orbital because the others are all filled, the next available atomic orbital is spherical and outside the others, The negative electron is held because there is positive charge in the nucleus. However most of the charge is already balanced by the electrons in the inner orbitals. This means the force of attractions is small and hence the orbital is large.