Different spectral lines of the Balmer series (transitions n → 2, with n being the
principal quantum number) fall one at a time on a Young's double slit apparatus.
The separation between the slits is d and the screen is placed at a constant distance
from the slits. What factor should d be multiplied by to maintain a constant fringe
width for various lines, as n takes different allowed values?
Options:
(A) n2 - 4
4n2
(B) n2 + 4
4n2
(C) 4n2
n2 - 4
(D) 4n2
n2 + 4
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.54)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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