Question

Given below are two statements: Statement (I): \textit{A spectral line will be observed for a 2p\(_x\) \(\rightarrow\) 2p\(_y\) transition.}
Statement (II): \textit{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 false but Statement II is true
• C. Statement I is true but Statement II is false
• 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

Step 1: In the case of degenerate orbitals (such as 2p\(_x\) and 2p\(_y\) orbitals in a hydrogen atom), transitions between them can occur and produce spectral lines. Hence, Statement I is correct. Step 2: However, Statement II is incorrect. The 2p\(_x\) and 2p\(_y\) orbitals are not degenerate in a real atom due to the presence of the electric field of the atom (i.e., their energies are slightly different). Thus, the correct answer is that Statement I is true and Statement II is false.