Which of the following elements has the smallest first ionization energy? How do you determine this? a. sodiumb. calcium c. potassium d. magnesium

Potassium (option C) has the smallest first ionization energy from the given elements.

Explanation:

First ionization energy is the energy required to separate one valence electron from an atom in gas phase.

The easier the atom can release the electron the lower the energy required to remove it, i. e. the lower the first ionization energy.

Sodium and magnesium are neighbor elements in the same period (period 3) of the periodic table. Sodium has one valence electron and magnesium has two valence electrons, both in the same principal energy level (n = 3). The valence electron of sodium is more easily removed than any of the two valence electrons from magnesium, due to the fact that the nuclear charge (number of protons) of the magnesium is greater than the nuclear charge of the sodium. As a general rule, in a period the nuclear charge increases from left to right, while the distance of the valence electrons from the nuclei is reduced, causing this that the first ionization energy increases from left to right down a period.

In conclusion the first ionization energy of sodium is smaller than the first ionization energy of magnesium, and the first ionization energy of potassium is smaller than the first ionization energy of calcium (these two elements are neighbors in the period 4).

Now you must compare the ionization energies of sodium and potassium, which are in the same group (column) : sodium is directly above potassium.

In a column, the first ionization energies generally decrease from top to bottom. Meaning, that the first ionization energy of potassium is smaller than the first ionization energy of sodium. The reason behind this trend is that when you go down a group the electrons occupy a larger orbital (further away from the nucleus) causing that electrons be further away from the nucleus), and so less energy is required to remove them.

In conclusion, potassium is the element from the list that has the smallest first ionization energy.