Why does Nitrogen form N₂ (and not N₄) while but Phosphorus forms P₄ (and not P₂)? $\ce{N2}$ is a gas
$\ce{P4}$ is a solid
$\ce{N}$ and $\ce{P}$ are in the same group in the periodic table

The bond enthalpies are:
$\ce{N#N}$ triple bond is $949~ \mathrm{kJ/mol}$

$\ce{P#P}$ triple bond is $490~ \mathrm{kJ/mol}$

$\ce{P-P}$ single bond is $200 ~ \mathrm{kJ/mol}$

$\ce{N-N}$ single bond is $159-296 ~ \mathrm{kJ/mol}$

So why does $\ce{P}$ go to $\ce{P4}$ not $\ce{P2}$ and why does $\ce{N}$ go to $\ce{N2}$ and not $\ce{N4}$?
Due to larger atomic size $\ce{P}$ is unable to form pi bonds and so it is tetra-atomic in which each $\ce{P}$ atom is linked with 3 other $\ce{P}$ atoms by 3 sigma bond. But, due to smaller atomic size $\ce{N}$ forms 1 sigma and 2 pi bonds i.e. triple bonds with other $\ce{N}$ atom and exists as diatomic molecule.






Reference: http://philmintz.tripod.com/Chemistry/page4.html