# In layman’s language what is the difference between stopping potential and work function?

In layman’s language what is the difference between stopping potential and work function? It feels like both the things mean the same thing, if I am wrong please explain the things to me.

Work function is the minimum energy required to liberate an electron from a solid to the space immediately outside the solid. Stopping potential is the electric potential difference between two locations required to prevent electrons from crossing that region. In a photoelectric experiment, these two quantities are related to each other, but they are not the same.

For instance, if electrons are liberated by photons of frequency $$\nu$$, the photons have energy $$h\nu$$, and if the work function of the solid the electrons are in is $$\Gamma$$, then the electrons can have a maximum kinetic energy of $$\frac{1}{2}mv^2 =h\nu-\Gamma$$. The maximum kinetic energy can be determined by varying the voltage difference on the gap between the solid and a current collector until the current reaches zero. The moment you reach a potential difference $$\phi$$ that stops the current, the maximum kinetic energy of the electrons is equal to the increase in potential energy of the electrons as they cross the gap, so $$e\phi=\frac{1}{2}mv^2$$. Putting this all together yields $$e\phi=h\nu-\Gamma$$ So varying the frequency of the light $$\nu$$ and measuring the corresponding stopping potential $$\phi$$ allows one to determine the work function $$\Gamma$$ and also Planck's constant $$h$$, but the stopping potential is clearly not the same thing as the work function.

• You have the opposite sign. Commented Jul 1 at 16:17
• Also, it would be far easier to simply say: The work function is a property of the metal and has nothing to do with the incoming light, whereas the stopping potential depends linear-affinely upon the colour of the light. They cannot be the same thing. Commented Jul 1 at 16:19