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Young's Modulus — Virtual Laboratory Y Elastica Lab Young's Modulus · Searle's Method Laboratory Instruments Graphs Data Undergraduate Physics · Elasticity Stretch a wire. Watch stiffness reveal itself. A full digital re-creation of the Searle's apparatus experiment — load a wire, measure its diameter under a micrometer, read its extension through a travelling microscope, and watch Young's modulus emerge from real measurement, not a lookup table. SVG apparatus Live Hooke's-law physics Stress–strain plotting Atomic-scale model Start the experiment → Read the aim The governing formula Y = F · L A · ΔL F — applied force (N) L — original length (m) A — cross-section area (m²) ΔL — extension (m) ...

Introduction to Energy Bands To understand the Kronig–Penney model and the origin of energy bands, we must first examine how electrons behave in isolated atoms and how their behavior changes when atoms come together to form a crystal. Isolated Atom vs Crystal An isolated atom contains electrons that occupy specific energy levels. According to quantum mechanics, electrons cannot possess arbitrary energies; instead, they are restricted to certain discrete energy states. For example, an electron in a hydrogen atom can occupy only specific energy levels such as E 1 , E 2 , E 3 , and so on. These levels are separated by forbidden energy regions where no electron states exist. Key Point: An isolated atom has discrete (quantized) energy levels. However, a crystal is made up of a very large number of atoms arranged in a regular repeating pattern known as a crystal lattice. In a typical solid, the number of atoms is of the order of 10 23 . When these atoms are brought clo...