(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the de Broglie wavelength of an 8 MeV proton.

2. Relevant equations

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

3. 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?

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# De Broglie wavelength of an electron

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