# Changing frequency of light without changing its energy

Three observations were detected in the photo-electric effect:

1. The kinetic energy of the ejected electrons doesn't change if you change the intensity of light (instead more electrons are ejected with the same kinetic energy)

2. There is a certain value of frequency below which no electrons are ejected

3. The kinetic energy increases if we increase the frequency of light.

The solution to these observations was given by Einstein who said that light consists of a finite number of energy quanta(carriers of energy) which are absorbed or emitted as units. These quanta are called photons and have energy equal to E=hf.

Therefore, if we increase the intensity, more photons are sent, and eventually, more electrons are ejected (since every electron needs a photon to be ejected) with no change in the kinetic energy.

This is what I've understood from the photo-electric effect chapter.

But I still can not understand how can we increase frequency without increasing the energy because I see from E = hf that frequency and energy are proportional.

• I don't understand how you conclude "increase frequency without increasing the energy" from all the rest? That's not happening, so there is nothing to understand. Mar 11, 2023 at 20:11
• @Raskolnikov the contradiction I saw is between observations 1 and 3. When I asked the professor how can these two observations be true with this relationship between energy and frequency he said that we can always increase the frequency of light without increasing its energy and he gave more explanation about electromagnetic waves. I didn't conclude it, I took it as a given but I still can not understand why. Mar 11, 2023 at 20:19

## 1 Answer

The energy of a single photon is given by $$E=hf$$, but the total energy of the light is given by $$E=nhf$$, where $$n$$ is the number of photons. You can change the intensity independently of the frequency by changing the number of photons, and you can change the frequency independently of the intensity by inversely changing the number of photons, keeping $$nhf$$ constant.