Key idea

When an electron emits a photon, it moves from a higher energy level to a lower energy level.

The energy of the emitted photon is $E_{\gamma} = E_{\text{initial}} - E_{\text{final}}$

So, the photon with the most energy corresponds to the largest downward energy gap.

Interpretation of the labeled transitions

From the given energy-level diagram, among the transitions labeled $i, ii, iii, iv$, we compare the vertical drop in each case.

• A larger downward jump $\Rightarrow$ larger energy difference
• Larger energy difference $\Rightarrow$ more energetic emitted photon

Identify the largest downward transition

From the diagram, transition $iii$ represents the greatest drop from a higher energy level to a lower energy level.

Therefore, it gives the maximum photon energy.

Match with options

• A: $iv$
• B: $iii$
• C: $ii$
• D: $i$

Hence, the correct option is $\boxed{B}$

Comparison with stored correct answer

Stored correct answer: B

Our derived answer: B

So, they agree.