Considering the $x$-axis as the internuclear axis,which of the following will not form a sigma $(\sigma)$ bond and why?
$(a)$ $1s$ and $1s$
$(b)$ $1s$ and $2p_{x}$
$(c)$ $2p_{y}$ and $2p_{y}$
$(d)$ $1s$ and $2s$

(C) $2p_{y}$ and $2p_{y}$ orbitals will not form a sigma $(\sigma)$ bond.
Since the $x$-axis is the internuclear axis,the $2p_{y}$ orbitals are oriented perpendicular to the internuclear axis.
Therefore,$2p_{y}$ and $2p_{y}$ orbitals will undergo lateral (sideways) overlapping,resulting in the formation of a pi $(\pi)$ bond instead of a sigma $(\sigma)$ bond.