Find the de Broglie wavelength of an 8 MeV proton.
y = h/p
where y is the wavelength
p = mv
K = Eo/sqrt(1-v^2/c^2)
where Eo is the rest mass and K is the kinetic energy
The Attempt at a Solution
I make the assumption that "an 8 MeV proton" is an proton with a kinetic energy of 8 MeV.
I know K = 8 MeV and Eo = 938.3 MeV. So I solve for v, get
v = sqrt(1 - (Eo/(K+Eo))^2)c = 0.1297554914c
I know m = 938.3 MeV/c^2. So I plug into p = mv and get
p = 121749577.6 eV/c
I know h = 4.136*10^-15 eV*s. So I plug into y = h/p and get
y = 3.397*10^-23 s*c
But I want nanometers, so since I know that c has units of m/s, I divide by the numerical value of c and multiply by 10^9 so that
y = 1.133*10^-22 nm
But this much too small, isn't it? Where am I going wrong?