Let us analyze the two statements in the context of atomic orbitals and electronic transitions:

Statement (I)

“A spectral line will be observed for a $ 2 p_x \rightarrow 2 p_y $ transition.”

For an emission (or absorption) line to be observed, there must be a difference in energy between the initial and final states.

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 degenerate—i.e., they all have the same energy.

Consequently, a transition from $2 p_x$ to $2 p_y$ (both having the same energy) would involve no energy change. Hence, no photon is emitted or absorbed for this “transition.” So you would not observe a spectral line for such a transition.

Therefore, Statement (I) is false.

Statement (II)

“$2 p_x$ and $2 p_y$ are degenerate orbitals.”

Orbitals within the same subshell (e.g., $2p$ subshell) are typically degenerate (same energy) in an isolated atom (especially a hydrogen-like atom).

Thus, $2 p_x$ and $2 p_y$ (and $2 p_z$) do indeed have the same energy.

Therefore, Statement (II) is true.

Conclusion

Statement (I): False

Statement (II): True

Hence, the correct choice is:

Option A: Statement I is false but Statement II is true.