Question

The radius of the Zr atom is 145 picometers. However the radius of the element directly below it, Hf, is only 144 pm. Think about this and select the following statements that are true.

1. This is the expected periodic trend for atomic radius.

2. This is not the expected periodic trend for atomic radius.

3. Based on the radii, the effective nuclear charge experienced by the valence electrons must slightly greater for Zr than for Hf.

4. Based on the radii, the effective nuclear charge experienced by the valence electrons must slightly greater for Hf than for Zr.

5. Slater\'s rules cannot explain this difference in radius.

6. Slater\'s rules can explain this difference in radius.

7. Hf is slightly smaller than Zr because: The 4f electrons in Hf do not shield as effectively as the inner electrons in Zr.

8. Hf is slightly smaller than Zr because: Most of the electron density for the f electrons in Hf is found nearer to the nucleus than for p and d orbitals.

Answer 1

The following are all the statements that are true with explanations.

Statement 2:This is not the expected periodic trend for atomic radius.

The Atomic radius trend is as we go down a group, atomic radius increases. This should be because the valence electrons occupy higher levels due to the increasing quantum number (n). So the valence electrons are further away from the nucleus as ‘n’ increases. Electron shielding prevents these outer electrons from being attracted to the nucleus; thus, they are loosely held, and the resulting atomic radius is large.

Statement 3 : Based on the radii, the effective nuclear charge experienced by the valence electrons must slightly greater for Zr than for Hf.

As Shielding effect causes reduction in the effective nuclear charge on the electron cloud, due to a difference in the attraction forces of the electrons on the nucleus.

Statement 5: Slater\'s rules can explain this difference in radius.

Slater's rules provide numerical values for the effective nuclear charge concept It showcases the shielding experienced by an s- or p- electron and the shielding experienced by a d- or f- electron.

Statement 7 :Hf is slightly smaller than Zr because: The 4f electrons in Hf do not shield as effectively as the inner electrons in Zr.

This can be linked to influence of lanthanide contraction on the post lanthanides in the periodic table. Lanthanide contraction is explained basis shielding effect. Generally electrons are added to the outer shells in multi electron atoms. And when electrons are added then the electrons already present shield the outer electrons from nuclear charge which makes them experience a lower effective charge on the nucleus. The order of s,p,d,f by shielding effect exerted by the inner electrons is  s > p > d > f . When particular subshell is filled in a period, atomic radius decreases. And this is predominant in lanthanides, as the 4f subshell which is filled across these elements is not very effective at shielding the outer shell (n=5 and n=6) electrons. Hence shielding effect is less able to counter the decrease in radius caused by increasing nuclear charge.