Which of the following atoms has the largest radius?

For neutral atoms, the periodic trends in atomic size can be described like this

Atomic size decreases when going from left to right across a period,
Atomic size increases when going from top to bottom down a group.

Let's use these trends to try and figure out which atom would have the largest radius.

If you look at elements that are located in the same group, potassium will have a larger atomic radius when compared with sodium. Likewise, bromine will have a larger atomic radius when compared with chlorine.

Now focus on potassium and bromine. Since potassium is located at the start of period 3, and bromine at the end of the same period, potassium will have a larger atomic radius than bromine, and thus the largest atomic radius of the four given atoms.