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 :

We are given two statements about atomic orbitals and transitions. We need to evaluate their truth and choose the correct option.

First, consider Statement (II): $$2p_{x}$$ and $$2p_{y}$$ are degenerate orbitals.

Degenerate orbitals have the same energy. In hydrogen-like atoms (without external fields), orbitals with the same principal quantum number $$n$$ and azimuthal quantum number $$l$$ are degenerate. For $$n=2$$ and $$l=1$$ (p-orbitals), the orbitals $$2p_x$$, $$2p_y$$, and $$2p_z$$ all have identical energy. Therefore, $$2p_x$$ and $$2p_y$$ are degenerate.

Thus, Statement (II) is true.

Now, consider Statement (I): A spectral line will be observed for a $$2p_{x}\rightarrow 2p_{y}$$ transition.

Spectral lines arise from transitions between different energy levels, where a photon is emitted or absorbed due to a non-zero energy difference. Since $$2p_x$$ and $$2p_y$$ are degenerate (same energy), the energy difference $$\Delta E = 0$$. Hence, no photon is emitted or absorbed, and no spectral line is observed.

Additionally, electric dipole transitions follow selection rules. The change in azimuthal quantum number must be $$\Delta l = \pm 1$$. Here, both orbitals have $$l=1$$, so $$\Delta l = 0$$, which violates the selection rule. This confirms the transition is forbidden.

Therefore, Statement (I) is false.

In summary:

• Statement (I) is false.
• Statement (II) is true.

The correct option is B: Statement I is false but Statement II is true.