# Video: Applying Knowledge of Ionization Energies and Atomic Radii

For statements I and II, state for each if they are true or false. I) Sodium has a larger first ionization energy than nitrogen. II) Nitrogen atoms have larger atomic radii than sodium atoms. If both are true, state if II is a correct explanation for I.

05:11

### Video Transcript

For statements I and II, state for each if they are true or false. I) Sodium has a larger first ionization energy than nitrogen. II) Nitrogen atoms have larger atomic radii than sodium atoms. If both are true, state if II is a correct explanation for I.

The first ionization energy of an element like sodium or nitrogen is the energy required to remove the outer electron from an atom of that element. The outer electron of a sodium atom in its ground state sits in the 3s subshell. Sodium sits on the periodic table in group one, so it has a single valence electron. And we know that valence electron is in the third shell because sodium is in the third period.

So, what about an atom of nitrogen? An atom of nitrogen in its ground state has the electron configuration 1s² 2s² 2p³. Nitrogen, being in group 15, has five valence electrons, two in the 2s subshell and three in the 2p subshell. If the nuclear charge is the same, an electron further from the nucleus is going to be easier to remove because it’s less strongly attracted to the nucleus. However, it will be harder to remove an electron from a more positive nucleus.

So, let’s think about the outer electron for sodium and nitrogen atoms. For sodium, we’re taking away an electron from the 3s subshell. This electron is further from the nucleus than the 2p electrons of a nitrogen atom. However, the nucleus of a sodium atom contains 11 protons, but the nucleus of a nitrogen atom only contains seven. So, we need to figure out which factor is more important.

It’s a general rule of thumb that the distance from the nucleus is more critical than the charge of the nucleus itself. We can rely on Coulomb’s law to prove this, which tells us that the force between particles of opposite charge is inversely proportional to the square of their separation, while the force is only proportional to the positive charge.

Alternatively, we can introduce the shielding effect of the inner shell electrons. The eight core electrons of a sodium atom reduce the effective nuclear charge felt by the 3s¹ electron, while a nitrogen atom only has two core electrons. This gives us an effective nuclear charge of three for the 3s electron in a sodium atom and an effective nuclear charge of five for the 2p electrons in a nitrogen atom.

When we look at all these factors combined, we can be pretty confident that sodium will actually have a smaller first ionization energy than nitrogen. So, statement I is false. If you’re interested, the value for the first ionization energy of sodium is 495.8 kilojoules per mole, while the value for nitrogen is almost three times greater, at 1402.3 kilojoules per mole. Now, we can move on to statement II.

Statement II says that nitrogen atoms have larger atomic radii than sodium atoms. As we mentioned while discussing statement I, an atom of nitrogen has the electron configuration 1s² 2s² 2p³ with a nucleus that contains seven protons. While an atom of sodium has an electron configuration of 1s² 2s² 2p⁶ 3s¹ with a nucleus that contains 11 protons.

The key difference when discussing atomic radii is the principal quantum number for the valence shell. In this case, the valence shell of sodium is the third electron shell, while the valence shell of nitrogen is the second. A sodium atom has a more positive nucleus than a nitrogen atom, so the 1s, 2s, and 2p subshells are closer to the sodium nucleus than they are to the nitrogen nucleus. However, that electron in the third shell makes a sodium atom bigger than a nitrogen atom. The slightly larger nuclear charge doesn’t offset that extra size from the third electron shell.

So, in fact, statement II is false. Nitrogen atoms actually have smaller atomic radii than sodium atoms. The atomic radius of a nitrogen atom is about 56 picometres, while the radius of a sodium atom is much greater at 190 picometres. A picometre is 10 to the minus 12 metres, so 10 to the 12 picometres is equivalent to one metre. Since both statements are false, the last part of the question does not need to be addressed. Statement II cannot be a correct explanation for statement I since both are false.