An electron moves at a velocity of 1.5 * 10⁸ m/s. Its de Broglie wavelength equals the wavelength of a photon. What is the ratio of the kinetic energy of the electron to the energy of the photon?

Correct answer: 1/4

Solution

Same wavelength: lambda. For photon: E = hc/lambda. For electron: lambda = h/(mv), so E_photon = hc/(h/mv) = mvc. KE_electron = (1/2)mv² (non-relativistic approximation). Ratio = (1/2)mv² / mvc = v/(2c) = (1.5e8)/(2*3e8) = 1.5/6 = 1/4.

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