An electron has the same de Broglie wavelength as the wavelength of a 1.8 eV photon.What is the speed of the electron? (m_electron = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J) A)1,100 m/s B)980 m/s C)910 m/s D)840 m/s E)770 m/s

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Quizplus · Accepted Answer

The de Broglie wavelength of an electron is given by λ = h/p, where h is Planck's constant and p is the momentum of the electron. The energy of a photon is given by E = hc/λ, where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. Given that the electron and the photon have the same wavelength, we can equate their energies to find the speed of the electron. The energy of the photon is 1.8 eV, which is 1.8 * 1.60 × 10^-19 J. Using the relation E = 0.5 * m * v^2 for the electron, where m is the mass of the electron and v is its speed, we can solve for v. Substituting the given values and solving for v gives a speed of approximately 1,100 m/s.

An Electron Has the Same De Broglie Wavelength as the Wavelength