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Allyl cyanide molecule contains:
A. 9 sigma bonds, 4 pi bonds and no lone pair
B. 9 sigma bonds, 3 pi bonds and one lone pair
C. 8 sigma bonds, 5 pi bonds and one lone pair
D. 8 sigma bonds, 3 pi bonds and two lone pair
E. 6 sigma bonds, 2 pi bonds and four lone pair

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Hint: A sigma bond is formed by the head on overlapping of half filled atomic orbitals along the internuclear axis. Formation of sigma bonds involves either s-s overlapping or s-p overlapping or p-p overlapping.
On the other hand, a pi bond is formed by the sidewise overlapping of half filled atomic orbitals in a direction perpendicular to the internuclear axis. It involves only p-p sideways overlapping.

Complete step by step answer:
A sigma bond can be formed independently between two atoms but a pi bond can be formed only when a sigma bond has already been formed between two atoms. This means every single bond will contain one sigma bond. Every double bond will also contain one sigma bond. But in a double bond, one pi bond will also be present in addition to the sigma bond. Similarly, in a triple bond, there will be a sigma bond and two pi bonds.
Let us now check the structures of the given compound allyl cyanide and determine the number of sigma and pi bonds present in it.
Allyl cyanide has the following structure.

Its structure has a cyanide group attached to an allyl group.
Let us first calculate the number of sigma and pi bonds between carbon and another carbon. There are two single bonds and one double bond between carbon-carbon. This means there are 3 sigma bonds and one pi bond between carbon-carbon.
Now, let us calculate the number of sigma and pi bonds between carbon and hydrogen. There are 5 single bonds between carbon and hydrogen which means there are 5 carbon-hydrogen sigma bonds and no pi bonds.
Now, let us calculate the number of sigma and pi bonds between carbon and nitrogen. Each cyanide group has a triple bond or one sigma and two pi bonds. Therefore, there are 1 sigma bond and 2 pi bonds between carbon and nitrogen.
There is also one lone pair on the nitrogen atom.
Thus, overall there are 9 sigma bonds, 3 pi bonds and one lone pair in allyl cyanide.

So, B is the correct answer.

Note: Sigma bonds are strong bonds as orbitals overlap to a greater extent but pi bonds are weak as the orbitals overlap to less extent. There is free rotation of atoms about the sigma bond but no free rotation about the pi bond. Moreover, the shape of a molecule is decided by the number of sigma bonds and it does not depend upon the pi bonds.