What is (a) the wavelength of a 5.40-ev photon and (b) the de broglie wavelength of a 5.40-ev electron?

(a) for a photon, the relationship between frequency f and energy E is
(1)
where h is the Planck cosntant.

First, we need to convert the energy from eV to Joule:


Then, using (1) we can find the frequency of the photon:


and finally we can find its wavelength:


(b) now we have to find the De Broglie wavelength of an electron with same energy of the previous photon. Again, we must convert the energy in Joules first:


Then we can use the relationship between momentum p and energy E of a particle, to find p: (electron mass:  )



And finally we can use De Broglie relationship to find the wavelength of the electron:

The answer is orbit around nucleus