Word Count : 296

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To show that Bose's derivation of Planck’s law for energy density is given by: \[ U_{v} dv = \frac{8\pi h}{c^{3}} \frac{v^3}{\exp\left(\frac{hv}{k_B T}\right) - 1} dv \] we proceed step by step: --- ### Step 1: Expression for the Number of Modes per Unit Volume The number of electromagnetic wave modes per unit volume in the frequency range \( v __________ ________ _______ _______ _________ _______ __________ _________ ______.
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