Question

How to derive the equation for stopping voltage of a photoelectron, i.e, K.E._max = | eV_o | ?

How to derive the equation for stopping voltage of a photoelectron, i.e,
`KE_max = | eV_o |` ?

Answer 1

We know that Stopping potential is that value of retarding potential difference needs to be applied between two plates which is just sufficient to halt the most energetic photo electrons emitted from the photoelectric material.

We need to equate maximum kinetic energy `K_max` of the photo-electron (having charge `e`) to the stopping potential `V_0`.

We know that
`"Electric potential energy"="Potential Difference"xx"Charge"`
In our case

`U=V_0xxQ`

To stop the most energetic photo-electron

`U=K_max`
`:.|V_0xxe|= K_max`
`=>K_max = |eV_0|`

Sign of magnitude is used as kinetic energy and electric potential energy are equal and opposite.

When charge `e` is stated in coulomb, the energy is calculated in joules. When charge is given as elementary charges, the energy will be calculated in electron volts eV.