What potential difference is needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10^-12 m? A)411 V B)206 V C)1650 V D)617 V

Question

Quizplus · Accepted Answer

The de Broglie wavelength of a particle is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. The momentum of a proton is given by p = mv, where m is the mass of the proton and v is its velocity. The kinetic energy of a proton is given by K = 1/2 mv^2. The potential difference needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10^-12 m is given by V = K/q, where q is the charge of the proton. Substituting the given values into these equations, we get:λ = h/p = (6.626 × 10^-34 J s)/(1.673 × 10^-27 kg * v) = 2.00 × 10^-12 mv = λp/h = (2.00 × 10^-12 m * 1.673 × 10^-27 kg)/(6.626 × 10^-34 J s) = 5.05 × 10^6 m/sK = 1/2 mv^2 = 1/2 * 1.673 × 10^-27 kg * (5.05 × 10^6 m/s)^2 = 2.12 × 10^-14 JV = K/q = (2.12 × 10^-14 J)/(1.602 × 10^-19 C) = 132.3 VTherefore, the potential difference needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10^-12 m is 132.3 V, which is closest to choice A, 411 V.

What Potential Difference Is Needed to Accelerate a Proton from Rest