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Why does the stability of hydrides decrease down the group in nitrogen family? Does this have to do with the fact that $\ce{NH3}$'s $\ce{N}$ is hybridised ($\ce{sp^3}$) while the rest of the group prefers unhybridised central atom for hydrogens leading to steric replusion in $\approx 90^{\circ}$ alignment of $\ce{H}$s?

Other possible explanation:

Perhaps, the orbital overlap order is: $\ce{2sp^3-1s > 1s-3p> 1s-4p>1s-5p> 1s-6p}$ which leads to greater stability of $\ce{NH3}$ over the others.

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The increasing size of the elements play a role here along with the overlapping factor.

Bismuth is humongous as compared to hydrogen so it's hydride is unstable. However nitrogen being small in size can form strong bonds with hydrogen. This also accounts for the fact that the reducing nature of the hydrides increase down the group.

As far as overlapping is concerned the bonds in the hydrides are - $\ce{2p-2p}$ up to $\ce{5p-2p}$.

Clearly the upper hydrides will be more stable as they have more effective overlapping between the orbitals.

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