Question

Which atom has the largest radius: oxygen; potassium; magnesium; sodium?

Answer 1

`"Potassium.........."`

Explanation:

Atomic size decreases across a Period, from left to right as we face the Table, and INCREASES down a Group, a column of the Periodic Table.

So here fourth period potassium is MANIFESTLY larger than third period magnesium and sodium, which are in turn LARGER than Group 17 oxygen....

And note here we consider the NEUTRAL atoms....NOT the molecules, and NOT the ions..........

And I hope there is a Periodic Table in front of you now. You should get familiar with it......

So which is larger? The potassium or bromine atom?

Answer 2

Potassium

Explanation:

An atom's size is defined by the distance from the nucleus to the valence (outer) shell of electrons. Although difficult to to actually measure, due to electrons existing in a probability field with no defined boundaries, it is common knowledge that the more valence shells of an atom, the larger the atom.
https://en.wikibooks.org/wiki/High_School_Chemistry/Atomic_Size

Knowing this, lets look at the electron configuration of the elements mentioned:
Oxygen = 2,6
Sodium = 2,8,1
Magnesium = 2,8,2
Potassium = 2,8,8,2
As we can see, only Potassium has four electron shells, therefore Potassium has the largest atomic size.

Alternatively, one can look at a Van der Waal radii table to find that the radii of the four elements are (in picometres):
Oxygen = 152 pm
Sodium = 227 pm
Magnesium = 173 pm
Potassium = 275 pm
Showing once again how Potassium has the largest atomic radius, and therefore the largest atomic size. Interestingly enough, Sodium has a larger atomic radius then magnesium, despite having less electrons and protons.
http://periodictable.com/Properties/A/VanDerWaalsRadius.v.html

I hope I helped!