Question

If particle A has a velocity 2 times higher than particle B, and half its mass, 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

The de Broglie wavelengths of particle A and particle B are the same because particle A has a velocity 2 times higher than particle B and half its mass, leading to the same momentum for both particles.

Step-by-step explanation:

The question asks how the de Broglie wavelengths of two particles compare if particle A has a velocity 2 times higher than particle B, and A has half the mass of B. The de Broglie wavelength, λ, is inversely proportional to the particle's momentum, p, which is the product of its mass, m, and velocity, v. Thus, the de Broglie wavelength is given by λ = h/(mv).

Since particle A has double the velocity and half the mass of particle B, we can set up the ratio of their velocities as VA = 2VB and their masses as mA = 1/2mB. The momentum for particle A becomes pA = (1/2 * mB) * (2 * VB) = mB * VB, which is the same as the momentum, pB, for particle B. Therefore, the de Broglie wavelength for both particles would be the same since they have equal momentum.

Answer: c) Both have the same wavelength.