Question

Out of the following transitions in hydrogen atom, identify the transition which emits photons of highest frequency.

• A. $n = 1$ to $n = 2$
• B. $n = 2$ to $n = 1$
• C. $n = 2$ to $n = 6$
• D. $n = 6$ to $n = 2$

Hint:

For highest emitted frequency, choose the transition with maximum downward energy drop.

Answer 1

The Correct Option is B

Concept:
Photon is emitted only when electron moves from higher level to lower level. Frequency of emitted photon is: \[ \nu=\frac{\Delta E}{h} \] So the highest frequency corresponds to the largest energy drop. ip

Step 1: Identify emitting transitions.
Emission occurs in: \[ 2\to 1 \] and \[ 6\to 2 \] The transitions \[ 1\to 2 \quad \text{and} \quad 2\to 6 \] are absorption transitions. ip

Step 2: Compare the energy drops.
Energy levels of hydrogen are: \[ E_n=-\frac{13.6}{n^2}\text{ eV} \] For \[ 2\to 1: \quad \Delta E=13.6\left(1-\frac14\right)=10.2\text{ eV} \] For \[ 6\to 2: \quad \Delta E=13.6\left(\frac14-\frac{1}{36}\right) \] \[ =13.6\left(\frac{8}{36}\right)=13.6\cdot \frac{2}{9}\approx 3.02\text{ eV} \] So the larger energy drop is for: \[ 2\to 1 \] ip Hence, the correct answer is:
\[ \boxed{(B)\ n=2\to n=1} \]