India · Examinations
India: Engineering & Physical Sciences
Prepare for GATE, CSIR-UGC NET/JRF, IIT JAM, JEST and TIFR with concept-focused physics and engineering learning, guided practice and exam pathways.
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PhysicsMaterials ScienceAI & MLMechanical Engineering
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GATE•CSIR-UGC NET/JRF•IIT JAM•JEST•Subject GRE•University & Graduate Learning•GATE•CSIR-UGC NET/JRF•IIT JAM•JEST•Subject GRE•University & Graduate Learning
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If lattice spacing doubles, what happens to first Brillouin-zone width?
LIVE CONCEPT EXPERIENCEREAL SPACE ↔ RECIPROCAL SPACE
G = 2π/a · −π/a ≤ k ≤ +π/a
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DISCOVER SOMETHING TODAY THE SCIENCE EDITION
Curiosity changes everything.
Remarkable moments, beautiful physics, and ideas that reshaped our understanding of the world.
Explore the extraordinaryThree stories to spark your next question
01 / HISTORY OF SCIENCEA discovery by observation 1928 ↗
30-SECOND DISCOVERY01 MIN READ
The accidental observation that transformed medicine.
A contaminated culture plate became evidence that one microorganism could inhibit another—an observation that helped open the antibiotic era.
A small observation. A profound scientific impact.02 / OPTICS & NATUREColor beyond pigment ↗
SCIENCE BEHIND THE COLOR
Brilliant color, without ordinary pigment.
Microscopic structures can shape reflected light and produce striking colors.
03 / FRONTIER MATERIALSOne layer. New behavior. ↗
MATERIALS THAT SURPRISE
When a material becomes atomically thin.
Reducing dimensionality can reveal properties unlike those of bulk materials.
✦ Observe · Question · UnderstandMORE STORIES COMING AS THE LIBRARY GROWS
WATCH & LEARN · ORIGINAL SCIENCE MICRO-LESSONS
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01 / SOLID STATE PHYSICS · FREE · 0:10
Reciprocal space
Increasing the real-space lattice spacing a reduces reciprocal spacing G = 2π/a. The video shows both changing together.
Notice the opposite changes in the two lattices.
Narration transcript
When lattice spacing increases, reciprocal spacing decreases. The reciprocal lattice vector is two pi divided by a.
02 / STATISTICAL MECHANICS · FREE · 0:10
Speed distributions
For a classical gas, increasing temperature broadens the Maxwell–Boltzmann speed distribution and moves its most probable speed upward.
Look for the broader curve and the shift of its peak.
Narration transcript
At higher temperature, particles move faster on average. The speed distribution broadens, and its peak shifts toward higher speeds.
03 / MATERIALS SCIENCE · FREE · 0:10
Crystal symmetry
A square lattice is unchanged by a 90° rotation about a lattice point. This is an example of fourfold rotational symmetry.
The atomic pattern coincides after one quarter-turn.
Narration transcript
Rotate a square lattice by ninety degrees. Its arrangement matches the original, revealing fourfold rotational symmetry.
✦ PRO MICRO-LESSON
Unlock the first Brillouin zone
04 / ADVANCED SOLID STATE · PRO · 0:10
First Brillouin zone
In a two-dimensional square reciprocal lattice, the first Brillouin zone is the central Wigner–Seitz cell, bounded halfway to the nearest reciprocal lattice points.
Identify the central cell and its reciprocal-space boundaries.
Narration transcript
The first Brillouin zone is the central cell of reciprocal space. Its boundaries occur halfway to neighboring reciprocal points.
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