(a) an electron has kinetic energy 5.00 ev. find its wavelength.

First, we need to convert electron's kinetic energy into Joules. Keeping in mind that 

we have


The kinetic energy of the electron is equal to:

where m is the electron mass and v its speed. If we re-arrange this equation, we can find the electron speed:


And now we can use De Broglie's relationship to find the electron's wavelength:

where h is the Planck constant and p=mv is the electron momentum. Substituting numbers, we get