De Broglie Wavelength Of An Accelerated Charged Particle
De Broglie Wavelength Of An Accelerated Charged Particle — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
de Broglie Wavelength of an Accelerated Charged Particle This formula is applicable for calculating the de Broglie wavelength of charged particles (like electrons, protons, alpha particles) accelerated from rest by an electric potential, strictly in the non-relativistic regime. The work done by the electric field on charge 'q' through potential 'V' is W = qV. This work appears as kinetic energy K. Thus, K = qV. The relationship between momentum 'p' and kinetic energy 'K' is p = sqrt(2mK). Substitute K = qV into the momentum equation: p = sqrt(2mqV). Using the de Broglie hypothesis, wavelength lambda = h / p. Substitute p to get lambda = h / sqrt(2mqV). The velocity of the particle must be much less than the speed of light (v << c). The particle must be accelerated from rest (initial kinetic energy = 0). The particle must have a non-zero charge (not applicable to neutrons). Confusing the potential 'V' (Volts) with velocity 'v' (m/s) in the denominator. Assuming this formula applies to neutral particles like neutrons (which cannot be accelerated by electric fields). Forgetting to convert units (e.g., using eV for energy without converting to Joules if using SI h). Applying this form when the particle has initial kinetic energy.