Given below are two statements :

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

Statement (II) : $2 \mathrm{p}_x$ and $2 \mathrm{p}_y$ are degenerate orbitals.

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

<p>Let us analyze the two statements in the context of atomic orbitals and electronic transitions:</p> <hr /> <h2>Statement (I)</h2> <blockquote> <p>“A spectral line will be observed for a $ 2 p_x \rightarrow 2 p_y $ transition.”</p> </blockquote> <p><p>For an emission (or absorption) line to be observed, there must be a difference in energy between the initial and final states.</p></p> <p><p>In a typical hydrogen-like or many-electron atom (without additional external fields or splitting effects), the three $2p$ orbitals ($2 p_x$, $2 p_y$, $2 p_z$) are <em>degenerate</em>—i.e., they all have the same energy.</p></p> <p><p>Consequently, a transition from $2 p_x$ to $2 p_y$ (both having the same energy) would involve <strong>no energy change</strong>. Hence, <strong>no photon</strong> is emitted or absorbed for this “transition.” So you <strong>would not</strong> observe a spectral line for such a transition.</p></p> <p>Therefore, <strong>Statement (I)</strong> is <strong>false</strong>.</p> <hr /> <h2>Statement (II)</h2> <blockquote> <p>“$2 p_x$ and $2 p_y$ are degenerate orbitals.”</p> </blockquote> <p><p>Orbitals within the same subshell (e.g., $2p$ subshell) are typically degenerate (same energy) in an isolated atom (especially a hydrogen-like atom).</p></p> <p><p>Thus, $2 p_x$ and $2 p_y$ (and $2 p_z$) do indeed have the same energy.</p></p> <p>Therefore, <strong>Statement (II)</strong> is <strong>true</strong>.</p> <hr /> <h2>Conclusion</h2> <p><p><strong>Statement (I)</strong>: <strong>False</strong> </p></p> <p><p><strong>Statement (II)</strong>: <strong>True</strong></p></p> <p>Hence, the correct choice is:</p> <blockquote> <p><strong>Option A: Statement I is false but Statement II is true.</strong></p> </blockquote>