# Why emission of an electron does not depend on light's intensity?

There's something that confuses me about the photoelectric effect. In an article I read, it's stated that the emission of an electron does not depend on the light's intensity. I'm not sure on which parameters does the light intensity depend on, after an online search I found this connection: $$I = \frac{1}{2}E h$$ where I is the intensity, $$E$$ is the energy and $$h$$ is planck's constant. when I see this formula, and consider the following one as well: $$E = h\nu$$ where $$E$$ is the energy of the photon, $$h$$ is planck's constant and $$\nu$$ is the light's frequency. I can write the light's frequency as a function of the intensity.

what I don't understand is, if the emission of the electron experimentally is independent of the light's intensity, and depend solely on the light's frequency, why is this connection: $$I = \frac{1}{2}h^2\nu$$ is wrong? or why can't I use it in order to calculate if electron will be emitted depending on the intensity?

I just want to emphasis: I'm not talking about the number of emitted electrons, I consider only the question whether a specific electron will break free from the atom or not.

• IMHO the independence of intensity is the result of first-order perturbative treatment. It is approximatelly independent of intensity. As the intensity increases you will have to include second-order (nonlinear) and higher-order processes. Then you will get dependence on intensity. In the future, I would suggest using LATEX for equations. – Cryo Oct 1 '19 at 8:57
• @Cryo thank you for your response, I understand your explanation, sound logical. I'll read about it. and I just downloaded LATEX, so next time I'll make sure to use it. – E. Ginzburg Oct 1 '19 at 9:56
• Where did you find the relation between Intensity and energy? A quick search only revealed relations where intensity is related to energy flow or energy density. In general there seems to exist more than one definition for intensity. As Rob Jeffries already pointed out there is something wrong with the dimensions in your relation. – Hartmut Braun Oct 1 '19 at 10:27
• @HartmutBraun your're right, I did see few formulas for intensity. I don't remember exactly on which site I saw this one, but it got me very confused. thank you everyone for helping me to solve this confusion! – E. Ginzburg Oct 1 '19 at 10:44

If the intensity of the light is changed, without changing the frequency, this merely reflects the number of photons present, and not their individual energies. i.e. $$I \propto N h\nu,$$ where $$N$$ is something like photons per second per unit area.
The formula you have written down is dimensionally incorrect. The units of energy are Joules and the units of the Planck constant are Joule-seconds. So your intensity has units of J$$^2$$s, which doesn't make sense.