Question

Why nitrogen exist as diatomic molecule $$\left(N_2\right)$$ and Phosphorus as $$P_4$$

Answer 1

Hint: Atomicity of the molecule is determined by the number of atoms present in the molecules. We know that Helium, Argon, Neon, etc, are noble gas atoms which are mono-atomic, they can exist without the formation of the bond with other molecules but other exist in di, tri, tetra, polyatomic form that depends on the number of electrons required to complete the octet

Step by step answer:
Nitrogen and phosphorus are present in the same group of the periodic table that is in the fifth group. The atomicity is different for different molecules based on the number of electrons present in the outermost shell of the atom. The octet rule says that the valence electron should have eight electrons in the valence shell of the atoms in the given molecule then, the molecule is said to attain stability.

The nitrogen and the phosphorus atoms are present in the p-block in the fifth group. The atomic number of Nitrogen is$$7$$ and electronic configuration is $$N:\left[He\right]2s^{2}2p^3$$ it will require one electron to complete the octet so, it will form covalent bond with another nitrogen atom to complete the octet.

Hence two atoms of nitrogen will come closer and form a triple bond by sharing six electrons. In nitrogen $$1{s^2}_{}2{s^2}_{}2{p^1}_{x}2{p^1}_{y}2{p^1}_z$$ from these orbitals $$2{p^1}_x$$ will from the one $${\sigma }_{p-p}$$bond and $$2{p^1}_{y}2{p^1}_z$$will form two$${\pi }_{p-p}$$bond.

The atomic number of phosphorus atom is $$15$$and electronic configuration is as you can see the electron is in third orbit and it is far from the nucleus as the size of phosphorous is larger than that of nitrogen.so it will form bond with other three phosphorous and orient themselves in tetrahedral shape each phosphorus will have two electrons as lone pain only three electron will take part in bond formation.

Hence, the size difference and the atomic number is responsible for difference in the structure of the molecules, nitrogen exist as diatomic molecule $$\left(N_2\right)$$ and Phosphorus as $$P_4$$.

Note: Here one should not get confused because both of them belong to the same group and have different atomic numbers so it will change the property.