A proton has a speed of 7.2 x $10^4$ m/s. What is the energy of a photon that has the same wavelength as the de Broglie wavelength of this proton? (m_electron = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s) A) 230 keV B) 150 keV C) 300 keV D) 370 keV E) 440 keV

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Quizplus · Accepted Answer

The de Broglie wavelength of the proton is given by:$$\lambda = \frac{h}{p} = \frac{h}{mv}$$where h is the Planck constant, p is the momentum of the proton, m is the mass of the proton, and v is the speed of the proton.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 the Planck constant.Since the photon has the same wavelength as the de Broglie wavelength of the proton, we have:$$\lambda = \frac{h}{p} = \frac{hc}{E}$$Solving for E, we get:$$E = \frac{p^2}{2m}$$Substituting the given values, we get:$$E = \frac{(7.2 	imes 10^4 	ext{ m/s})^2}{2(9.11 	imes 10^{-31} 	ext{ kg})}$$$$E = 230 	ext{ keV}$$Therefore, the correct answer is A.

A Proton Has a Speed of 7 10410^4104 M/s What Is the Energy of a Photon That Has

A Proton Has a Speed of 7 $10^4$ M/s What Is the Energy of a Photon That Has