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

Explanation:

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 spped of light in vacuum

Finally:

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explanation: