How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 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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Quizplus · Accepted Answer

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 momentum of the electron:$$\frac{h}{p} = \frac{hc}{E}$$$$p = \frac{E}{c}$$We can then use the momentum of the electron to find its velocity:$$v = \frac{p}{m}$$where m is the mass of the electron.Plugging in the given values, we get:$$v = \frac{3.4 	ext{ eV} 	imes 1.60 	imes 10^{-19} 	ext{ J/eV}}{9.11 	imes 10^{-31} 	ext{ kg} 	imes 3.00 	imes 10^8 	ext{ m/s}} = 2000 	ext{ m/s}$$Therefore, the correct answer is A.

How Fast Must a Nonrelativistic Electron Move So Its De