(C) In $CH_2 = CH - CH = CH_2$ ($1$,$3$-butadiene),all four carbon atoms are $sp^2$ hybridized.$sp^2$ hybridized carbon atoms have a trigonal planar g

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(C) In $CH_2 = CH - CH = CH_2$ ($1$,$3$-butadiene),all four carbon atoms are $sp^2$ hybridized.$sp^2$ hybridized carbon atoms have a trigonal planar geometry.Since all carbon atoms are connected in a conjugated system,the entire molecule lies in a single plane.Therefore,the shape of the molecule is planar.