How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (mel = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J) A) 2000 m/s B) 1900 m/s C) 1700 m/s D) 1600 m/s E) 1400 m/s

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The de Broglie wavelength of an electron is given by:$$\lambda = \frac{h}{p}$$where h is Planck's constant and p is the momentum of the electron. The momentum of a photon is given by:$$p = \frac{E}{c}$$where E is the energy of the photon and c is the speed of light.We can set the de Broglie wavelength of the electron equal to the wavelength of the photon and solve for the speed of the electron:$$\frac{h}{p} = \frac{hc}{E}$$$$p = \frac{E}{c}$$$$v = \frac{p}{m} = \frac{E}{mc}$$$$v = \frac{(3.4 	ext{ eV})(1.60 	imes 10^{-19} 	ext{ J/eV})}{(9.11 	imes 10^{-31} 	ext{ kg})(3.00 	imes 10^8 	ext{ m/s})}$$$$v = 2000 	ext{ m/s}$$

How Fast Must a Nonrelativistic Electron Move So Its De