Consider the following three particles:
1) a free electron with speed v₀
2) a free proton with speed v₀
3) a free proton with speed 2v₀
Rank them according to the wavlengths of their matter waves, least to greatest.

Question

Quizplus · Accepted Answer

The wavelength of a particle's matter wave, according to the de Broglie hypothesis, is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. The momentum p is given by the product of the mass m and velocity v of the particle. Since a proton is much more massive than an electron, for the same velocity, a proton's momentum will be much greater, resulting in a shorter wavelength. Therefore, a proton moving at speed v will have a shorter wavelength than an electron moving at the same speed, and a proton moving at 2v will have an even shorter wavelength due to its increased momentum. Thus, the correct ranking from least to greatest wavelength is: 3 (proton at 2v), 2 (proton at v), 1 (electron at v).

Consider the Following Three Particles