Young's double slit experiment is performed using a beam of C60 (fullerene)
molecules, each molecule being made up of 60 carbon atoms. When the slit
separation is 50 nm, fringes are formed on a screen kept at a distance of 1 m from
the slit s. Now, t he experiment is repeated with C70 molecules with a slit
separation of 92.5 nm. The kinetic energies of both the beams are the same. The
position of the 4th bright fringe for C60 will correspond to the nth bright fringe
for C70. What is the value of n (rounded off to the nearest integer) ?
Options:
(A) 5
(B) 6
(C) 7
(D) 8
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.44)**
**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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