# Why is the increase in covalent radius from As to Bi not as big as from N to P?

The following is the radius of Group $$15$$ elements:

$$\begin{array}{c|c} \hline \text{Element} & \text{Covalent Radius }(\pu{pm}) \\ \hline \ce{N} &75 \\ \ce{P} &110 \\ \ce{As} &121 \\ \ce{Sb} &140 \\ \ce{Bi} &155 \\ \hline \end{array}$$ Source: General Properties and Reactions. (2020, August 15). Retrieved April 6, 2021, from https://chem.libretexts.org/@go/page/31730

From the above table it is clear that the increase in radius decreases as we go down the group.

## My Attempt to Reason it

The electronic configurations of $$\ce{N, P}$$ and $$\ce{As}$$ are:

• $$\ce{N: [He]} \ \mathrm{2s^2 2p^3}$$
• $$\ce{P: [Ne]} \ \mathrm{3s^2 3p^3}$$
• $$\ce{As: [Ar]} \ \mathrm{4s^2 3d^10 4p^3}$$

### First let us compare $$\ce{N}$$ and $$\ce{P}$$

$$\ce{P}$$ has $$\ce{8 e-}$$s and $$\ce{8 p+}$$s more than $$\ce{N}$$. The $$\ce{8 p+}$$s increase the nuclear charge. But, due to the addition of $$\ce{e-}$$s, the shielding effect also increases i.e., there is more repulsions caused by the core $$\ce{e-}$$s.

Out of the $$\ce{8 e-}$$s, $$3$$ goes into $$\mathrm{2p}$$, $$2$$ goes into $$\mathrm{3s}$$ and $$3$$ goes into $$\mathrm{3p}$$. The shielding effect due to $$\mathrm{s}$$ and $$\mathrm{p}$$ is appreciable. As a result, the effective nuclear charge is not that high. But due to the addition of extra shell i.e., $$3$$, the size increases by almost $$\pu{35 pm}$$.

### Now Let us compare $$\ce{P}$$ and $$\ce{As}$$

Now in $$\ce{As}$$, there are $$18 \ce{e-}$$s and $$18 \ce{p+}$$s more than that in $$\ce{P}$$. Out of the $$18 \ce{e-}$$s, $$3$$ goes into $$\mathrm{3p}$$, $$2$$ goes into $$\mathrm{4s}$$, $$10$$ goes into $$\mathrm{3d}$$ and $$3$$ goes into $$\mathrm{4p}$$.

In this case, majority of the $$\ce{e-}$$s are in the $$\mathrm{3d}$$ orbital. The shielding effect due to $$\mathrm{3d}$$ is not much. In fact, the order of the ability of orbitals to shield is: $$\mathrm{s} \gt \mathrm{p} \gt \mathrm{d} \gt \mathrm{f}$$

Due to this, the effective nuclear charge is more and therefore the size doesn't increase as much as it increase on going from $$\ce{N}$$ to $$\ce{P}$$.

Is my reasoning correct? If not, what is the reason behind this?