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I've been told that the definition of intensity of any radiation is 'the energy crossing unit area in unit time.' So, I understand that if we increase the number of photons passing through an area by keeping their energy constant, the intensity increases. But, my doubt is let's say if we kept the number of photons passing through a fixed area constant and increased their energy (by increasing frequency), will the intensity increase? I think it should increase according to the definition. But in books, it says it doesn't increase. What's the correct explanation for this?

In this question, the answer is (A)&(B). Why isn't the (C) option correct too? If more energetic photons are emitted then intensity of light should increase.

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Intensity is the total amount of energy falling (or going through) per unit area per unit time i.e, $\frac{J}{m^2.s}$.

For monochromatic radiation,

$Total\space energy = Number\space of\space photons\space \times Energy\space of\space one\space \space photon$

and $E_{photon}=h\nu$

$Intensity = \frac{Number\space of\space photons\space \times Energy\space of\space one\space \space photon}{At}$

$I=\frac{nh\nu}{At}$ $\tag{1}$

For constant area and time,

$I \propto n.\nu$

This is a very important result. You can increase the intensity of the radiation by either increasing the number of photons in it or increasing energy of each photon, or both.

As for option (C), if you increase energy of each photon but decrease the number of photons emitted by the source per unit time by the same factor then the intensity will remain the same as before. For instance, if the number of photons emitted by the source per unit time is halved, doubling the intensity will give you the same intensity as before.

This is evident from equation (1). Therefore, option (C) is not necessarily correct but (A) and (B) are.

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Perhaps it is not mentioned in books that with increase in frequency of radiation intensity does not increase. In fact increasing frequency of radiation means we have taken a source of radiation of higher power and with increase in power of the source, intensity of radiation will increase. I think that you have a confusion that with increase in frequency and keeping the number of photons srtiking a given area of the surface, photoelectric current with increase or not. It will not increase because during Photoelectric effect photons o suffer one-to-one perfect inelastic collision with electrons. So one Photon can eject only one electron in spite of its large energy content and hence photo electric current will not increase.

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There are many ways of defining the intensity of light, but if you are just measuring the energy per unit time per unit area then yes increasing the frequency while keeping the number of photons constant will increase the intensity. If your book says otherwise you need to provide us with a link to the book so we can check it, or maybe post a photo of the relevant part of the book.

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  • $\begingroup$ Can you explain the (C) option? I'm thinking that if more energetic photons are emitted then the intensity of light should increase. BTW the answer is only (A)&(B) $\endgroup$ – user157725 Aug 14 '17 at 7:32
  • $\begingroup$ @user157725: the question asks what happens if the intensity of the light source is increased. While it isn't explicitly stated, this implies that every else remains unchanged i.e. the frequency doesn't change. In that case the photon energy cannot change. $\endgroup$ – John Rennie Aug 14 '17 at 7:51
  • $\begingroup$ Surely the only one that's always true is (B); whether (A) and (C) are true depends on how the increase in intensity was achieved (frequency and/or number of photons). And (D) is always false. $\endgroup$ – innisfree Aug 14 '17 at 9:23

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