Question

Estimate the wavelength (in nm) of such a proton moving at 2.81x10^8 m/s (mass of a proton = 1.673x10^-27 kg).

Answer 1

To look at a particle as a wave, we need to us the de Broglie equation...\[\lambda = \frac{h}{mv}\]Where...

Lambda is the wavelength.
h is Planck's constant
m is the mass of the particle, and
v is the velocity of the particle

This is easy enough. It's already solved for the value we want to find, so we can just plug in some numbers...\[\lambda = \frac{6.626*10^{-34}J*s}{(1.673*10^{-27}kg)(2.81*10^{8}m*s^{-1})}\]
All of the units cancel appropriately to give us the wavelength in meters...\[\lambda = 1.41m*10^{-15}*(\frac{1*10^9nm}{1m})=1.41*10^{-6}nm\]