Lithium is an element from group 1 and in the second period, having an atomic number of 3. While potassium is an element from group 1 as well but in the 4th period, having an atomic number of 19.
Some properties can be expected just by the position of an element in the periodic table, such as ionization energy, atomic and ionic radius, electronegativity, and others.
Let's analyze each option to discover the correct one.
Atomic radius and ionic radius: The atomic radius will be greater for elements with a greater number of electronic shells and with an effective nuclear charge that does not affect the size of the atom. The ionic radius follows the same trend. The atomic radius will be greater for elements from right to left and top to bottom in the periodic table.
Since K is two periods under Li, K has a bigger atomic and ionic radius.
First ionization energy: The ionization energy refers to how much energy is needed to remove one electron from the outer shell of a specific element. The fewer electronic shells, the higher the ionization energy since electrons are closer to the nucleus and suffer a higher force of attraction to it.
Since K has up to the 4th electronic shell and Li has only 2 electronic shells, Li has the highest ionization energy.
Number of protons: The number of protons is the same as the atomic number. If K has an atomic number of 19 and Li of 3, that means K has more protons than Li.
Final answer after all that was explained:
c. first ionization energy.