A nonrelativistic electron has a kinetic energy of 5.4 eV.What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J) A)2.4 keV B)2.2 keV C)2.0 keV D)2.5 keV E)2.7 keV

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Quizplus · Accepted Answer

The de Broglie wavelength of the electron is given by:$$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}}$$where h is Planck's constant, p is the momentum of the electron, m is the mass of the electron, and K is the kinetic energy of the electron.The energy of a photon is given by:$$E = hf = \frac{hc}{\lambda}$$where f is the frequency of the photon, c is the speed of light, and h is Planck's constant.Substituting the de Broglie wavelength into the equation for the energy of a photon, we get:$$E = \frac{hc}{\lambda} = \frac{hc}{\frac{h}{\sqrt{2mK}}} = \sqrt{2mK^2c^2}$$Substituting the given values, we get:$$E = \sqrt{2(9.11 	imes 10^{-31} 	ext{ kg})(5.4 	ext{ eV})(1.60 	imes 10^{-19} 	ext{ J/eV})^2(3.00 	imes 10^8 	ext{ m/s})^2}$$$$E = 2.2 	ext{ keV}$$Therefore, the correct answer is A.

A Nonrelativistic Electron Has a Kinetic Energy of 5