Was working on a problem with electrons acting as waves in diffraction. Part of the question asked me to calculate the momentum of the electron. Since I was dealing with waves I used the following equation:
$h=pλ \implies p = h/λ$
Since $λ = v/f$ we can substitute that in, resulting in $p = hf/v$.
Substituting in the de Broglie $h = E/f$ into the above equation we get $p = E/v$. Since we're talking about electrons the only energy that the electron has is kinetic so we can substitude $E = 0.5mv^2$ into the equation giving us $p = 0.5mv^2/v = 0.5mv$.
I've repeat that, $p = 0.5mv$. Any 4th-grade physicist knows that momentum is $mv$ so on one hand, I have mv and on the other I have a derivation saying the momentum is $0.5mv$. Is there a mistake in my derivation I'm not seeing?
P.S: I noticed something a bit later. $p = E/v \implies E = pv = mv^2$. See any similarities between this and another infamous equation in the realm of relativity?