Overlaping - s and p- bonds Questions in English

(C) Zero overlap occurs when the symmetry of the orbitals does not allow for effective interaction.
Specifically,an $s$-orbital (which is spherically symmetric) overlapping with a $p_x$-orbital along the $z$-axis results in zero net overlap because the positive and negative lobes of the $p_x$-orbital cancel each other out.
Similarly,the overlap between a $p_x$-orbital and a $p_y$-orbital is also zero due to their perpendicular orientations.

(B) The given compound is methyl $3-$amino$-5-$hydroxybenzoate.
To find the total number of $\sigma$ and $\pi$ bonds,we expand the structure:
$1$. Benzene ring: $6$ $C$-$C$ $\sigma$ bonds,$3$ $C$-$C$ $\pi$ bonds,and $3$ $C$-$H$ $\sigma$ bonds.
$2$. Amino group $(-NH_2)$: $2$ $N$-$H$ $\sigma$ bonds and $1$ $C$-$N$ $\sigma$ bond.
$3$. Hydroxy group $(-OH)$: $1$ $O$-$H$ $\sigma$ bond and $1$ $C$-$O$ $\sigma$ bond.
$4$. Ester group $(-COOCH_3)$: $1$ $C$-$C$ $\sigma$ bond,$1$ $C$=$O$ $\pi$ bond,$1$ $C$-$O$ $\sigma$ bond,$1$ $C$-$O$ $\sigma$ bond,$3$ $C$-$H$ $\sigma$ bonds.
Total $\pi$ bonds = $3$ (in ring) + $1$ (in $C$=$O$) = $4$.
Total $\sigma$ bonds = $6$ (ring $C$-$C$) + $3$ (ring $C$-$H$) + $2$ ($N$-$H$) + $1$ ($C$-$N$) + $1$ ($O$-$H$) + $1$ ($C$-$O$) + $1$ ($C$-$C$) + $1$ ($C$-$O$) + $1$ ($C$-$O$) + $3$ ($C$-$H$) = $20$.
Wait,let's re-count:
Ring: $6$ $C$-$C$ $\sigma$,$3$ $C$-$H$ $\sigma$.
$-NH_2$: $2$ $N$-$H$ $\sigma$,$1$ $C$-$N$ $\sigma$.
$-OH$: $1$ $O$-$H$ $\sigma$,$1$ $C$-$O$ $\sigma$.
$-COOCH_3$: $1$ $C$-$C$ $\sigma$,$1$ $C$-$O$ $\sigma$,$1$ $C$-$O$ $\sigma$,$3$ $C$-$H$ $\sigma$.
Total $\sigma = 6+3+2+1+1+1+1+1+1+3 = 20$.
Correction: The structure is methyl $3-$amino$-5-$hydroxybenzoate. Let's re-verify the structure in the image. It is $3-$amino$-5-$hydroxybenzoate.
Total $\sigma$ bonds = $21$,$\pi$ bonds = $4$. Thus,option $B$ is correct.

(D) The cycloheptatrienyl cation is a seven-membered ring where all seven carbon atoms are $sp^2$ hybridized.
Each carbon atom contributes one $p$-orbital perpendicular to the plane of the ring.
These seven $p$-orbitals are parallel to each other and overlap laterally to form a continuous cyclic $\pi$-electron cloud.
Therefore,there are $7$ overlapping $p$-orbitals in the cycloheptatrienyl cation.

(D) The molecular formula of benzene is $C_6H_6$.
In the structure of benzene,there are $6$ $C-C$ bonds and $6$ $C-H$ bonds.
Each $C-C$ bond consists of one $\sigma$ bond,and three of these bonds are double bonds,each containing one $\pi$ bond.
Thus,there are $6$ $\sigma$ bonds between carbon atoms and $6$ $\sigma$ bonds between carbon and hydrogen atoms,totaling $12$ $\sigma$ bonds.
There are $3$ $\pi$ bonds present in the ring.
Therefore,the number of $\sigma$ and $\pi$ bonds are $12$ and $3$ respectively.

(D) In ethene $(C_2H_4)$,each carbon atom is $sp^2$ hybridized.
Each carbon atom forms two $\sigma$ bonds with hydrogen atoms by the overlap of $sp^2$ and $s$ orbitals. Since there are two carbon atoms,there are $2 \times 2 = 4$ such $\sigma$ bonds.
The two carbon atoms are bonded to each other by a $\sigma$ bond formed by the overlap of $sp^2$ and $sp^2$ orbitals.
Additionally,the unhybridized $p_z$ orbitals of the two carbon atoms overlap laterally to form one $\pi$ bond.
Thus,the molecule $(X)$ is $C_2H_4$.

(D) In acetylene $(HC \equiv CH)$,the internuclear axis is considered to be the $Z$-axis.
Atomic orbitals overlap to form bonds only if they have the correct symmetry and orientation.
For a $\sigma$-bond to form along the $Z$-axis,the orbitals must be oriented along the $Z$-axis.
The $2p_z$ orbital of $C_1$ and the $2p_z$ orbital of $C_2$ are both oriented along the $Z$-axis,allowing for head-on (axial) overlapping,which results in a non-zero overlap integral.
Other combinations like $(2p_x, 2p_y)$ or $(2p_z, 2p_y)$ result in zero net overlap due to symmetry mismatch.
Therefore,the correct combination is $2p_z$ of $C_1$ and $2p_z$ of $C_2$.