Final answer:
The false statement is (c) that alkali metals have the largest first ionization energy in a row. Ionization energy increases from left to right across a period. Therefore, option (c) is the false statement.
Step-by-step explanation:
The statement that is false is (c) In a given row in the periodic table, the alkali metal always has the largest first ionization energy. This is incorrect because first ionization energy typically increases across a period from left to right, meaning that the alkali metals (which are on the left side of a period) have the lowest ionization energies, not the highest.
As for the other statements: (a) The first ionization energy of bromine is indeed larger than that of calcium, since calcium is an alkaline earth metal and bromine is a non-metal further to the right on the same period; (b) Barium, being further down on the periodic table than magnesium.
It has a smaller first ionization energy since ionization energy decreases down a group; and (e) The second ionization energy of an element is indeed always greater than the first, because it is more difficult to remove an electron from a positively charged ion than from a neutral atom.