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# Einstein's photoelectric equation

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## Einstein's photoelectric equation

Einstein looked at the way in which electrons tried to leave the metal. He established that it actually takes energy for an electron **to leave the surface of the metal**. He called this energy the **work function, Φ**.

He then applied the Conservation of Energy Principle for an electron receiving energy and leaving the metal. Compare energy received and used by the electron at the surface.

**Energy supplied to the electron = hf** (energy from the photon)

**Energy used by the electron is either:**

used as work function, Φ, to escape from the surface

or

is left with the electron after it has escaped, in which case it is in the form of E_{k}.

So for each electron at the surface which leaves the metal:

**Energy supplied = energy used**

Or

hf = Φ + E_{kmax}

**This is Einstein's Photoelectric Equation.**

The E_{kmax} is there because only those electrons on the surface will have the maximum kinetic energy on leaving.

Electrons from deep inside which make it to the surface and still have enough energy to escape will have used some energy getting to the surface. These electrons will therefore have less energy left once they are free of the metal and so they will have E_{k} less than the maximum possible.

Notice that if you consider the special case where the energy of the arriving photons is **hf _{o}** (i.e. the energy of the threshold frequency photons), even the electrons on the surface will only have enough energy to overcome the work function and no more.

So once they have escaped they will have no energy left. Their **E _{k} = zero**. In this case, the photoelectric equation becomes:

**hf _{0} = Φ**

This is a useful way of calculating the work function for a material.

**Also it allows you to rewrite the Photoelectric equation as follows:**

or