molecules - Why does ammonia have sp hybridization?

Apparently it has $sp^3$ hybridization, but I don't understand why. Ammonia ($\ce{NH3}$) seems to me to not require $sp$ hybridization because all of its bond lengths are already equal. It has 3 hydrogens bonded to the $p$ orbitals. Why can't the lone electron pair in nitrogen's $2s$ shell stay put where it is?

Answer

Well, I can think of these reasons that can justify the hybridization in ammonia molecule.

1. 
   

   Bond angle: If the molecule did not have hybrid orbits, and instead had unhybridized p-orbitals taking part in the bond formation, then the bond angle between the orbitals would be 90 degrees. And as for the real situation the bond angle is nearly 107 which makes the molecule more stable, decreasing the bond pair-bond pair and bond pair-lone pair repulsion.

   
   


2. 
   

   Energy: Recalling the definition of hybridization, it is the mixing of the atomic orbitals having slightly different energies to form new orbitals that have equal energies. This stabilizes the molecule. As for ammonia molecule due to hybridization the energies of the lone pair of electrons and the bond pair of electrons becomes almost equal, thereby increasing the stability of the molecule.

   
   


3. 
   

   Geometry: Thinking about the spatial arrangement of the atoms in the molecule of ammonia if there is no hybridization in the molecule then the size of the orbital containing lone pair of electrons would be different from that of the orbitals containing bond pair of electrons. Also if hybridization would not be taking place, explaining the geometry of the molecule, that is it's trigonal pyramidal shape, would not be possible.