What is the energy of a photon that has the same wavelength as an electron having a kinetic energy of 15 ev?

The kinetic energy of an electron is given by the following equation:

(1)

Where:

is the momentum of the electron

is the mass of the electron

From (1) we can find :

(2)

(3)

Now, in order to find the wavelength of the electron with this given kinetic energy (hence momentum), we will use the De Broglie wavelength equation:

(4)  

Where:  

is the Planck constant  

So, we will use the value of found in (3) for equation (4):

(5)  

We are told the wavelength of the photon is the same as the wavelength of the electron:

(6)  

Therefore we will use this wavelength to find the energy of the photon using the following equation:

(7)  

Where is the speed of light in vacuum

Finally: