Calculating the frequency of a free electron

[Turukano26]

I feel like I must be missing something obvious, but I can't figure it out. I have the speed of an electron, and to calculate its frequency i used p = h/λ, then subbed in p =mv and λ= v/f. Giving me the equation f = mv²/h. However, I also could use E = 1/2 mv² and E = hf to give me the equation f = mv²/2h. Where is this factor of two coming from??

 

[vsv86]

I am not entirely sure, but I think you have discovered the difference between phase and group velocities of the free electron.And, they are different. Griffiths has a great section on this (Griffiths "Introduction to Quantum Mechanics", Sec 2.4, Eq. 2.90).

Before proceeding you must tell us which "speed" do you mean. The phase velocity, or the group velocity.