JEE Advanced · Chemistry · 4. Chemical Bonding

For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $2 p_{z}$ orbitals is(are)

A $σ$ orbital has a total of two nodal planes.
B $σ^{*}$ orbital has one node in the $xz$ -plane containing the molecular axis.
C $π$ orbital has one node in the plane which is perpendicular to the molecular axis and goes through the center of the molecule
D $π^{*}$ orbital has one node in the $xy$ -plane containing the molecular axis.

Verified Solution

Answer & Solution

Correct Answer

(D) $π^{*}$ orbital has one node in the $xy$ -plane containing the molecular axis.

Step-by-step Solution

Detailed explanation

When this orbital combine along the internuclear axis then

σ

orbital is formed while this orbital approach each other parallel to each other and perpendicular to the internuclear axis

π

orbital is formed.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the

n^{t h}

orbit of the atom and List-II contains options showing how they depend on

n

List - I	List - II
(I) Radius of the $n^{t h}$ orbit	$(P)$ $\propto n^{- 2}$
(II) Angular momentum of the electron in the $n^{t h}$ orbit	$(Q)$ $\propto n^{- 1}$
(III) Kinetic energy of the electron in the $n^{t h}$ orbit	$(R)$ $\propto n^{0}$
(IV) Potential energy of the electron in the $n^{t h}$ orbit	$(S)$ $\propto n^{1}$
	$(T)$ $\propto n^{2}$
	$(U)$ $\propto n^{1 / 2}$

Which of the following options has the correct combination considering List-I and List-II?

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One mole of a monatomic ideal gas undergoes the cyclic process $\mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L} \rightarrow \mathrm{M} \rightarrow \mathrm{J}$, as shown in the P-T diagram.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.
[$\mathcal{R}$ is the gas constant.]

List-I	List-II
(P) Work done in the complete cyclic process	(1) $R T_0-4 R T_0 \ln 2$
(Q) Change in the internal energy of the gas in the process JK	(2) $0$
(R) Heat given to the gas in the process KL	(3) $3 K T_0$
(S) Change in the internal energy of the gas in the process MJ	(4) $-2 R T_0 \ln 2$
	$(5)-3 R T_0 \ln 2$

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For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two 2pz orbitals is(are)

Step-by-step Solution

For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $2 p_{z}$ orbitals is(are)