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Recently, my friend bemused me with a question related to the momentum of an electron. The confusing logic is stated below:

Since an electron is a particle and according to classical physics, we know that it's momentum equals to: $p_e=mv$

However, by looking from a different perspective, we found that, From de Broglie's hypothesis: $p=\frac{h}{\lambda} $
And since de Broglie proposed that particles also obey the Einstein relation: $E=hf$
Then, $p_e=\frac{hf}{c}=\frac{E_e}{v}$
Since the only energy of the electron is Kinetic energy,
then $E_e=\frac{1}{2}mv^2$
and $p_e=\frac{1}{2}mv$

We thus arrive at a contradiction: $mv \neq \frac{1}{2}mv $

What is the flaw in this logic?

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    $\begingroup$ You should be using relativistic kinematics, the total energy of the electron is not its kinetic energy only en.wikipedia.org/wiki/… $\endgroup$ – anna v Sep 19 '14 at 3:50
  • $\begingroup$ Minor correction - it is = rather than $\ne$ in the contradiction condition. $\endgroup$ – 299792458 Sep 19 '14 at 7:02
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    $\begingroup$ Essentially a duplicate of physics.stackexchange.com/q/34214/2451 $\endgroup$ – Qmechanic Sep 19 '14 at 7:46