Question

In the hydrogen atomic spectrum, the emission of the least energetic photon takes place during the transition from $n=6$ energy level to $n = $ _____ energy level.

• A. 1
• B. 3
• C. 5
• D. 4
• E. 2

Hint:

Closer energy levels → lower energy photon emitted.

Answer 1

The Correct Option is C

Concept: Energy transitions in hydrogen atom
---

Step 1: Energy formula
\[ E_n = -\frac{13.6}{n^2} \text{ eV} \] Energy difference: \[ \Delta E = E_f - E_i \] ---

Step 2: Least energetic photon
Smallest energy difference occurs when levels are closest. Thus transition: \[ 6 \rightarrow 5 \] ---

Step 3: Compare options

• $6 \rightarrow 1$ → large energy ❌
• $6 \rightarrow 2$ → large ❌
• $6 \rightarrow 3$ → moderate ❌
• $6 \rightarrow 4$ → smaller ❌
• $6 \rightarrow 5$ → smallest ✅ --- Final Answer: \[ \boxed{5} \]