Question

Given below are two statements:
Statement (I): A spectral line will be observed for a \(2p_x \rightarrow 2p_y\) transition.
Statement (II): \(2p_x\) and \(2p_y\) are degenerate orbitals.

In the light of the above statements, choose the correct answer from the options given below:

• A. Both Statement I and Statement II are true
• B. Statement I is true but Statement II is false
• C. Statement I is false but Statement II is true
• D. Both Statement I and Statement II are false

Hint:

For hydrogen-like atoms, the 2p orbitals (\( 2p_x, 2p_y, 2p_z \)) are degenerate in energy. However, in multi-electron atoms, degeneracy may be lifted due to the electric field and other interactions.

Answer 1

The Correct Option is C

Each statement is evaluated to determine its correctness.

1. Statement (I): A spectral line will be observed for a \(2p_x \rightarrow 2p_y\) transition.

   This statement is incorrect. Transitions between degenerate orbitals, such as \(2p_x\) and \(2p_y\), do not result in the emission or absorption of light. Spectral lines arise from energy level changes. As \(2p_x\) and \(2p_y\) are degenerate and possess identical energies, a transition between them involves no energy difference, thus producing no spectral line.

2. Statement (II): \(2p_x\) and \(2p_y\) are degenerate orbitals.

   This statement is correct. Degenerate orbitals share the same energy level. In an atomic context, the three 2p orbitals (\(2p_x\), \(2p_y\), and \(2p_z\)) are degenerate due to their belonging to the same energy level and experiencing equivalent potential energy within a spherically symmetric field.

Consequently, Statement I is false and Statement II is true.

Correct Answer: Statement I is false but Statement II is true.