Question

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

a) Particle A has a shorter wavelength
b) Particle A has a longer wavelength
c) Both have the same wavelength
d) Wavelength depends on speed, not mass

Answer 1

If particle A has a mass 2 times higher than particle B, and both have the same speed, then particle A has a shorter de Broglie wavelength than particle B.

Step-by-step explanation:

The de Broglie wavelength (λ) is the wavelength associated with a particle and is given by the equation λ = h / p, where h is Planck's constant and p is the momentum of the particle.

Since momentum is the product of mass (m) and velocity (v), and both particles have the same speed, the momentum of particle A is twice that of particle B because it has twice the mass. Therefore, particle A has a shorter de Broglie wavelength than particle B (λ = h / (2m * v) versus λ = h / (m * v)).