- #1

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Thank you in advance.

1. Homework Statement

1. Homework Statement

An electron has kinetic energy 3.50eV. Find it's wavelength.

## Homework Equations

(1) p=mv

(2) K=½m

**v**

^{2}

(3) p=E/c=h/λ

(4) E

_{r}=mc

^{2}

(5) E

_{total}=K+E

_{r}

## The Attempt at a Solution

Note: my prof said not to use relativistic equations, as the energy is not high enough, but we have covered relativity in this class.

I now know how to solve this problem:

I solved for the speed of the electron with the kinetic energy formula, and put it into the following:

λ=h/(m

**v**)

I got 0.656nm, which is correct.

My problem is that I did not initially solve the problem this way. What I did first was calculate the rest energy of the electron (E

_{r}=mc

^{2}) and add it to the kinetic energy to get the "total" energy. This was based off an equation which I was given by my prof: E

_{total}=K+E

_{r}. I then took that "total" energy and solved for the wavelength by deriving the equation: λ=hc/E from equation (3) above. I got the wrong answer, 0.00242nm, with this method.

What I don't understand is why my original method does not work. I'm assuming my fundamental understanding of these equations is wrong. Is the total energy of the electron

*not*the rest energy plus the kinetic energy? Is there something I'm missing? My professor was not helpful this time around, so I'm turning to you guys!

Thank you for your time.