An electron is accelerated from rest through a potential difference. After acceleration the electron has a wavelength of 880 nm. What is the potential difference responsible for the acceleration of the electron? (h = 6.626 × 10^-34J ∙ s, m_electron = 9.11 × 10-31 kg, e = 1.6 10^-19C) A) 1.9 × 10^-6 V B) 1.7 × 10^-6 V C) 2.2 × 10^-6 V D) 2.5 × 10^-6 V

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Quizplus · Accepted Answer

The de Broglie wavelength of an electron is given by:λ = h/pwhere:λ is the wavelengthh is Planck's constantp is the momentumThe momentum of an electron is given by:p = mvwhere:m is the mass of the electronv is the velocity of the electronThe kinetic energy of an electron is given by:KE = 1/2 mv^2where:KE is the kinetic energyThe potential difference through which an electron is accelerated is given by:V = KE/ewhere:V is the potential differencee is the charge of an electronSubstituting the expressions for p, KE, and V into the de Broglie wavelength equation, we get:λ = h/√(2meV)Solving for V, we get:V = h^2/(2meλ^2)Substituting the given values, we get:V = (6.626 × 10^-34 J s)^2/(2 × 9.11 × 10^-31 kg × (880 × 10^-9 m)^2)V = 1.9 × 10^-6 VTherefore, the correct answer is A.

An Electron Is Accelerated from Rest Through a Potential Difference