# Video: Applying Knowledge of the First Ionization Energies of Na and Mg and the Relationship between Ionization Energy and Atomic Radius

For statements I and II, state for each if they are true or false. I) The first ionization energy of Na is greater than the first ionization energy of Mg. II) In general, the ionization energy of an atom increases as the atomic radius decreases. If both are true, state if II is a correct explanation for I.

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### Video Transcript

For statements I and II, state for each if they are true or false. I) The first ionization energy of Na is greater than the first ionization energy of Mg. II) In general, the ionization energy of an atom increases as the atomic radius decreases. If both are true, state if II is a correct explanation for I.

First ionization energy is defined as the amount of energy required to remove one electron from each atom in a mole of those atoms in the gas phase to form a 1+ ion. Often, when we talk about ionization energy, we tend to discuss what is happening in one atom. But remember that the definition strictly refers to a mole of atoms. Let’s look at an example.

If we took magnesium atoms in the gaseous state and removed from each just one electron, we would end up with Mg¹⁺ ions. We can write this simply as Mg⁺ ions. The amount of energy required to remove this one electron from each of those atoms is the first ionization energy. In general, as we move from left to right across a period on the periodic table, there are more protons in the nucleus. But the number of electrons in the inner shells of the atoms in that same period are the same. So the force of attraction experienced by the outer or valence electrons increases as the number of protons in the nucleus increases.

We say that the effective nuclear charge increases as we move from left to right across the periodic table because of this increase in the number of protons in the nucleus. These trends as we move from left to right are general rules, but do not always apply. There are always exceptions to these types of rules. Effective nuclear charge can be defined as the net charge experienced by valence electrons in the outer shells. Effective nuclear charge has an influence on several things in atoms as well as ions.

Firstly, it influences the atomic or ionic radius and the ionization energy. The higher the effective nuclear charge, the more tightly and thus closely the outer electrons are held to the nucleus of the atom. This results in a decreasing atomic size as you move from left to right across a period. Secondly, the more tightly these valence electrons are held, the harder it is and the more energy required to remove one electron from the valence shell. And thus the first ionization energy increases as you move from left to right across a period.

In period or row three of the periodic table, we see that sodium is to the left of magnesium. So statement I is false. The first ionization energy of sodium is not greater, but is smaller than the first ionization energy of magnesium. And we have seen that statement II is true. In general, the ionization image of an atom does increase as the atomic radius decreases across a period or row on the periodic table. Because only one statement is true, we need not address the last statement.