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

To determine which statement is correct, let's evaluate each one separately.

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

   This statement is false. The transition between degenerate orbitals such as \(2p_x\) and \(2p_y\) does not lead to the emission or absorption of light. Spectral lines are observed when there is a change in energy levels. Since \(2p_x\) and \(2p_y\) are degenerate and have the same energy, a transition between these orbitals does not result in a change in energy and hence no spectral line is produced.

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

   This statement is true. Degenerate orbitals are those that have the same energy level. In an atom, the three 2p orbitals (\(2p_x\), \(2p_y\), and \(2p_z\)) are degenerate because they belong to the same energy level and experience the same potential energy in a spherically symmetric potential.

Based on the explanations above, we can conclude that Statement I is false, while Statement II is true.

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

Answer 2

To determine the correctness of the given statements, let's analyze each:

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

In atomic theory, spectral lines occur due to transitions between different energy levels of an electron within an atom. However, both \(2p_x\) and \(2p_y\) orbitals belong to the same energy level and sublevel, which means they are degenerate—having the same energy in an isolated atom without external fields. As there is no energy difference between them, a transition from \(2p_x\) to \(2p_y\) would not result in the emission or absorption of photons, and thus, no spectral line would be observed. Hence, Statement (I) is false.

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

This statement is true because \(2p_x\), \(2p_y\), and \(2p_z\) orbitals in an atom like hydrogen are degenerate (having the same energy). They only become non-degenerate (possessing different energies) under external conditions such as a magnetic or electric field or in multi-electron systems where electron-electron interactions are significant.

Given the analysis above:

Statement I	Statement II
False	True

Thus, the correct answer is: Statement I is false but Statement II is true.