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Semester IV โ€” Engineering Physics & Electrodynamics

NCERT Chapter 14: Quantum Mechanics & Dual Nature of Matter

According to wave-particle duality, matter exhibits wave-like behavior when in atomic or subatomic scale. The wavelength associated with an electron of mass m moving with non-relativistic velocity v is determined by Planck's quantum constant h. When subjected to an electrostatic potential difference V, the kinetic energy acquired is expressed as E_k = qV. Therefore, substitution into de Broglie relation yields the standard dispersion matrix:

Fundamental Derivation Expressionฮป = h / p = h / (m ยท v) | ฮ”x ยท ฮ”p โ‰ฅ โ„ / 2
Source S ----[Slit A]---> โ–‘โ–‘โ–‘โ–‘โ–‘ Screen Interference ----[Slit B]---> โ–‘โ–‘โ–‘โ–‘โ–‘ Fringe Width ฮฒ = (ฮป ยท D) / d

Further empirical observation confirms that under standard temperature and pressure (STP), the divergence between theoretical boundary conditions and numerical approximation reduces exponentially.

โ˜… NOTE: V.V. Important 5-mark derivation asked in 2024 End-Sem Exam. Do not skip diagram!
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