How many carbon-hydrogen bond orbitals are available for overlap with the vacant p-orbital in ethyl carbocation?
(a) 0
(b) 3
(c) 5
(d) 6

Hint: Carbocation is a species in which the carbon atom has a positive charge and can form three bonds. Stability of carbocation depends on the number of carbon atoms and functional groups attached to it.
Complete step by step solution:
-Ethyl carbocation is ethane in which one of the hydrogen is missing from one carbon and it has a positive charge on that carbon atom. The structure of ethyl carbocation is as shown in the figure below

-Now let us see how many p orbitals are there vacant in the carbocation.

There are two vacant orbitals. The carbon next to carbocation has carbon-hydrogen bonds. All the three are available for the overlap with the vacant orbital of the carbocation. The vacant p-orbital forms a partial overlap giving a partial sigma-pi conjugation. This can also lead to hyperconjugation. Hyper conjugation is the interaction of the electrons in a sigma bond (C-H or C-C) with adjacent empty or partially filled p orbital or pi orbital and it gives an extended molecular orbital which increases the stability of the system. It is not resonance.
Hence, the 3 carbon-hydrogen bonds are available for overlap with the vacant p-orbital of the ethyl carbocation. The correct answer to the question is option (b).
Note: Due to the vacant p orbital, carbocation is electron deficient. Because of this, it can act as an electrophile. Carbocation has a trigonal planar shape.