Question

how to calculate ratio of debroglies wavelength

Answer 1

This question is about group/phase velocities and also De Brogilie wavelength.

What I would like to know is how to derive ratio λe/λpλe/λp (λeλeand λpλp are De Broglie wavelength for electron and proton) if we know that electron and proton have same velocities?

I know that when we say "velocity" vv, this velocity is the same as "group velocity" vgvg. So for start I can calculate ratio for group velocities:

ve=vp⟶vgevge=vevp=1ve=vp⟶vgevge=vevp=1

and similarly I can do for phase velocities vpvp:

vpevpp=c2vgec2vgp=vgpvge=1vpevpp=c2vgec2vgp=vgpvge=1

But when i try to calculate the ratio for wavelengths I got stuck:

λeλp=hpehpp=pppe= ⟵I got stuck here where i don't knowhow to use relation 

Answer 2

Explanation:

The de Broglie equation is an equation used to describe the wave properties of matter or particles.

de Broglie suggested that particles can exhibit properties of waves, and proved that every moving particle has a matter wave associated with it.

The wavelength of the wave depends on the mass and the velocity of the particle:

λ=h\mv,

where:λ is wavelength in m.

h =6.626×10−34J.

⋅

h is Planck's constant.

m is the mass of a particle in kg moving at a velocity

v in m/s.