Atoms, which can be assumed to be hard spheres of radius R, are arranged in an fcc lattice with
lattice constant a, such that each atom touches its nearest neighbours. Take the center of one of the
atoms as the origin. Another atom of radius r (assumed to be hard sphere) is to be accommodated at
a position (0, a/2, 0) without distorting the lattice. The maximum value of r/R is ________. (Give
your answer upto two decimal places)
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.37)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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