IIT JAM Physics 2026 | FCC Packing Fraction Explained Step-by-Step#IITJAM2026#JAMPhysics #SolidState

In this video, we solve and explain an important FCC Packing Fraction problem from IIT JAM Physics 2026. The concept of packing fraction is a key topic in solid state physics and crystal structure, and it is frequently asked in competitive examinations such as IIT JAM Physics, CSIR NET Physics, JEST, TIFR GS, and GATE Physics. In crystalline solids, atoms are arranged in highly ordered patterns forming unit cells. One of the most important crystal structures is the Face Centered Cubic (FCC) lattice, which is commonly found in metals like copper, aluminum, silver, and gold. Understanding the packing efficiency of FCC structures helps students analyze how atoms occupy space inside a crystal. The packing fraction (or packing efficiency) is defined as the fraction of volume of the unit cell that is actually occupied by atoms. Packing Fraction = (Volume occupied by atoms in the unit cell) / (Total volume of the unit cell) For an FCC unit cell, atoms are located at: • 8 corner positions • 6 face-centered positions The effective number of atoms per FCC unit cell is: Number of atoms = 4 In FCC geometry, the relation between the atomic radius (r) and lattice parameter (a) is: a = 2√2 r Using this relation, the packing fraction of FCC structure becomes: Packing Fraction = π / (3√2) Numerically, Packing Fraction ≈ 0.74 This means 74% of the space in an FCC crystal is occupied by atoms, making it one of the most efficient packing arrangements in nature. Key concepts explained in this video include: • Structure of the Face Centered Cubic (FCC) lattice • Effective number of atoms in an FCC unit cell • Relation between atomic radius and lattice parameter • Derivation of the packing fraction formula • Comparison of FCC packing with other crystal structures • Short tricks to solve IIT JAM Physics crystal structure problems Many entrance exam questions test whether students can quickly determine the packing efficiency or identify the crystal structure using geometric relations. Understanding the FCC structure clearly makes it easier to solve these questions efficiently. This video is part of our IIT JAM Physics 2026 Complete Solution Series, where we solve real exam questions and explain the underlying concepts in a structured and exam-oriented way. The aim is to help students strengthen their fundamentals in solid state physics. This lecture will be especially useful for students preparing for: IIT JAM Physics CSIR NET Physics JEST Physics TIFR GS Physics GATE Physics MSc Physics Entrance Examinations At Dr. Sourav Sir’s Classes, we focus on conceptual clarity, exam-oriented preparation, and systematic discussion of previous year questions so that students can perform confidently in competitive exams. For academic guidance and coaching support: Website: www.souravsirclasses.com Contact: 9836793076