periodic trends - Why does screening effect decrease due to d-orbital?

In 13^th group, atomic radius increases from boron to aluminium. From aluminium to gallium, atomic radii decreases. From gallium to indium, atomic radii increases. And from indium to thallium, atomic radii decreases.

The reason for this irregular trend given is screening effect. While explaining my teacher told that due to d-orbital screening effect decreases.

I can't get why?

Answer

The reason d-orbitals make a difference is that electrons in d-orbitals do not screen nuclear charge as effectively as those in s and p orbitals. This is because of something called penetration .

The mathematical shapes of d-orbitals prevent them from allowing electrons to penetrate very closely to the nucleus, compared with electrons in s or p-orbitals. In gallium, you have $10$ electrons in the filled $3$d-subshell, and each of these electrons is doing a slightly worse job (relatively speaking) of screening the nuclear charge than the electrons in the s and p orbitals. Therefore, the effective nuclear charge in gallium is slightly higher than that in aluminum, so the increase in the radius is a quite a bit smaller than would be expected based on the difference between boron and aluminum, or gallium and indium.
The trend goes:

• 
  
  

  $\pu{82 pm}$ ($\ce{B}$)

  
  


• 
  

  $\pu{118 pm}$ $\ce{(Al)}$

  
  


• 
  

  $\pu{126 pm}$ $\ce{(Ga)}$

  
  


• 
  

  $\pu{144 pm \ce{(In)}}$

  
  
  

  [covalent radii from www.webelements.com].

  
  

This effect is generally known as the d-block contraction. (It can be more or less pronounced depending on how you define the atomic radii.)

A similar thing happens (in principle) when you go from indium to thallium; except in this case you are now dealing with adding a filled f-subshell to the valence shell.

Electrons in f-orbitals are even worse at screening nuclear charge than those in d-orbitals, therefore again, the effective nuclear charge in thallium is a bit larger than it is in indium, so again the jump in radius is fairly small (from $144$ to $148$ pm). This effect (of the filled f-subshell) is generally known as the lanthanide contraction.