Question

A metal emits electrons that possess a kinetic energy = `3.1 xx 10^-19` J/electron when exposed to radiation whose frequency is `2.4 xx 10^15` Hz. What is the threshold frequency of the metal in Hz?

Answer 1

I got: `f_"threshold"=1.93xx10^15Hz` but check my maths.

Explanation:

We know that the metal should emit electrons with kinetic energy `K` equal to the energy transported by the photons of light and given as:

`E=hf`

where `h` is Planck's Constant and `f` is the frequency; however, the electrons use a bit of the incoming energy to "free" themselves from the metal and we call this bit of energy the Work Function `phi`.

The threshold frequency will be the one that, carried by a photon, will give an energy that matches exactly the Work function (needed to free the electron BUT not to give it kinetic energy to actually fly away!).

So we get:

`K=hf-phi`

and when we have `K=0`

`0=hf_("threshold")-phi`

From the first, using our data, we get (for each electron):

`3.1xx10^-19=6.63xx10^-34*2.4xx10^15-phi`

so that rearranging:

`phi=1.28xx10^-18J`

into the second equation:

`0=6.63xx10^-34f_"threshold"-1.28xx10^-18`

rearranging:

`f_"threshold"=1.93xx10^15Hz`