Final answer:
Krypton (Kr) has the largest ionization energy among the given elements because it is a noble gas with a complete valence shell, making it very stable.
Step-by-step explanation:
The element with the largest ionization energy among Ca (calcium), Ni (nickel), Br (bromine), and Kr (krypton) is Kr, which is krypton. Ionization energy tends to increase across a period on the periodic table as the effective nuclear charge increases, and noble gases have the highest ionization energies within their periods due to their full valence shells, which make them very stable. Hence, krypton, being a noble gas, has the largest ionization energy among the given elements.