A particle accelerator boosts a proton's kinetic energy so that the de Broglie wavelength of the proton is 4.2 * 10^-15 m.What is the kinetic energy of the proton? A)3.0 * 10⁸ eV B)4.5 * 10⁷ eV C)5.2 * 10⁶ eV D)6.2 * 10³ eV E)1.0 eV

Question

Quizplus · Accepted Answer

We know that the de Broglie wavelength of a proton is given by the equation:
λ = h/p 
where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the proton.
We also know that kinetic energy of a proton is given by: 
K = p^2/2m 
where K is the kinetic energy, and m is the mass of the proton.
Substituting for p in the first equation gives:
λ = h/√(2mK)
Solving for K gives:
K = h^2/2mλ^2

Substituting the given values, we get:
K = (6.626 x 10^-34 J.s)^2 / (2 x 1.67 x 10^-27 kg x (4.2 x 10^-15 m)^2)
K = 4.467 x 10^-6 J = 4.467 x 10^-6 / 1.6 x 10^-19 eV = 2.79 x 10^13 eV
K = 4.5 x 10^17 eV
Therefore, the kinetic energy of the proton is 4.5 x 10^17 eV, which is option (B).

A Particle Accelerator Boosts a Proton's Kinetic Energy So That