Question

Two particles have the same mass. If particle A has a velocity 2 times higher than particle B, how do their de Broglie wavelengths compare?

a) Particle A has a longer wavelength
b) Particle A has a shorter wavelength
c) Both have the same wavelength
d) Wavelength comparison cannot be determined

Answer 1

Particle A has a shorter de Broglie wavelength compared to Particle B since the wavelength is inversely proportional to momentum, and Particle A has twice the velocity, thus a higher momentum than Particle B.

Step-by-step explanation:

When two particles have the same mass, and one particle (Particle A) has a velocity that is twice as high as the other particle (Particle B), we use the de Broglie hypothesis to compare their wavelengths.

According to the de Broglie hypothesis, the wavelength (λ) of a particle is inversely proportional to its momentum (p), which can be represented by λ = h/p, where h is Planck's constant. Since momentum is the product of mass (m) and velocity (v), p = mv, we know that if two particles have the same mass, the one with the higher velocity will have the higher momentum.

Therefore, Particle A, with twice the velocity of Particle B, will have a shorter de Broglie wavelength since wavelength is inversely proportional to velocity in this context. This makes b) Particle A has a shorter wavelength the correct answer for the comparison of their de Broglie wavelengths.