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If, $I=\frac{nh\nu}{/at}$, why does photocurrent does not increase on increasing frequency?

If same intensity and different frequency radiation is used, shouldn't $n_1\nu_1=n_2\nu_2$ hold true? [since $I$ is proportional to $n\nu$] Shouldn't $n_1>n_2$ (if $\nu_1<\nu_2$), and hence number of photons be different, therefore photocurrent different? Where I am getting it wrong? Why we only say number of photons determine intensity while explaining this?

Here, $\nu$ = frequency; $n$ = number of photons; $h$ = planck's constant; $at$ = area$\times$ time and $I$ = intensity.

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  • $\begingroup$ Could you define the symbols you've used? $\endgroup$
    – Cross
    May 19, 2022 at 8:52
  • $\begingroup$ PLaase use MathJax to format the mathematics. $\endgroup$
    – Toffomat
    May 19, 2022 at 8:55

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I think I understand what you're asking. It's, in fact, a big question that was raised when photoelectric effect was studied.

The intensity of a light beam is a measure of the photon density, while its "color" is a measure of the frequency of those photons. Those two quantities are, in fact, completely unrelated.

It was a puzzle a century ago, because physicists realized that, in order to ionize a gas, intensity wasn't the right parameter to play with: you could bombard the gas with high intensity light and nothing would happen in spite of the huge energy input, and you could use a weak intensity but high frequency light, and the gas would ionize.

The interpretation (in modern terms) is that light is made of photons, and a gas atom will only ionize if one photon brings enough energy to make an electron jump out of its energy level. If you raise the intensity without raising the frenquency, you'll have more photons, but each photon will still have the same energy.

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  • $\begingroup$ Is this formula I am using not applicable here, if its applicable then why we use 'intensity' when we talk about photocurrent, why don't we say photon flux? $\endgroup$ May 19, 2022 at 9:41
  • $\begingroup$ As far as I know, intensity for a light beam is defined as the photon flux. At least in every field I worked in or studied. It can include photon energy (for instance when its unit is watt), but as I explained it isn't enough to explain light's interaction with matter in some cases. $\endgroup$
    – Miyase
    May 19, 2022 at 10:05

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