Question

According to Slater's rules the effective nuclear charge of Beryllium and Sodium is 1.95 and 2.20 respectively.

That means that the outermost electron of Na feels a stronger attraction from the nucleus than the outermost electron of Be.

But we also know that the atomic radius of Be is smaller than Na and hence Be atom is smaller than Na. That means that the electrons of Be are closer to its nucleus so they must feel a greater attraction than the electrons of Na

The way i think about the above, somewhat contradictory statements, is that the pulling of the outermost electron in Na has to be bigger because there is also a greater shielding effect. Indeed the electron in the 3s orbital of Na feels a greater attraction than the 2s electron of Be but because of the inner electrons pushing it out it can't come closer to the nucleus and so Na ends up being bigger than Be. Is my way of thinking this right?

My question though has to do with the 1st Ionization energy of Be being greater than Na. Why is that? It's the effective nuclear charge that tells us how much attraction the electrons feel from the nucleus.

Answer 1

The atomic radius of Na is larger than Be's even with a higher Zeff, due to Na's outermost electron being in the higher 3s orbital compared to Be's 2s. Be has a higher first ionization energy because its valence electron is closer to the nucleus, experiences less shielding, and is thus more tightly held, despite Na's higher Zeff.

Step-by-step explanation:

The question pertains to effective nuclear charge (Zeff), atomic radius, and first ionization energy as they relate to the elements Beryllium (Be) and Sodium (Na).

Zeff is a measure of the net positive charge experienced by an electron in a multi-electron atom. Despite Na having a higher Zeff than Be, the atomic radius of Na is larger than Be's because Na's outermost electron is in the 3s orbital as opposed to Be's 2s orbital. The increase in the principal quantum number (n = 3 vs. n = 2) leads to a larger atomic radius due to the outer electron being further from the nucleus and experiencing more shielding from inner electrons.

Regarding first ionization energy, despite Na having a higher Zeff compared to Be, Be has a higher first ionization energy because the electron is being removed from a smaller atomic radius with less shielding, meaning it is more tightly held by the nucleus.