# Photoelectric effect problem

Aurora_b
Homework Statement:
Why KE_(max) depends on frequency but doesn't depend on intensity? (This isn't exactly my homework but a related conceptual doubt i have in order to solve the homework questions)
Relevant Equations:
So the confusion arose when my teacher wrote the equation for photoelectric effect:

KE_max = hf - W ------ eqn 1)
where,
KE_max = maximum kinetic energy of ejected electrons.
W= work function of the metal

Then the teacher wrote the formula for intensity
I = Nhf/A ------- eqn 2)

where,
N = no of photons incident per unit time
A= Area

Then the following statement was made:
Statement 1: KE_max depends on frequency but doesn't depend on Intensity.
I would believe the last statement if Intensity only depended on N but it also depends on the frequency f. Now if Intensity depends on f we can also find a relationship between KE_max and Intensity by substituting from eqn 2) in eqn 1)

KE_max = IA/N - W

So if KE_max depends on f and I depends on f then we can find the dependence between KE_max and I.

I understand I am wrong and that statement 1 is correct but I am just unable to convince myself, because everyowhere the reasoning is that I depends on N so it is independent but I also depends on f. Please help me understand.

Delta2

Homework Helper
Gold Member
2022 Award
KE_max = IA/N - W

So if KE_max depends on f and I depends on f then we can find the dependence between KE_max and I.

Consider your (correct) equation: KE_max = IA/N - W

Suppose you double the intensity. That means (using the concept of photons) that N must have doubled. So what happens to KE_max?

Delta2
Homework Helper
Suppose you double the intensity. That means (using the concept of photons) that N must have doubled. So what happens to KE_max?
Be careful.

If you double the intensity by doubling the frequency then you will increase KE_max.
If you double the intensity without changing the frequency then you will not.

When the text suggests that KE_max is independent of intensity, it is with the unstated assumption that frequency is being held constant. (e.g. you are shining two identical lights on the illuminated area, not switching from a red lamp to a blue).

Delta2 and Steve4Physics
Homework Helper
Gold Member
2022 Award
Be careful.

If you double the intensity by doubling the frequency then you will increase KE_max.
If you double the intensity without changing the frequency then you will not.

When the text suggests that KE_max is independent of intensity, it is with the unstated assumption that frequency is being held constant. (e.g. you are shining two identical lights on the illuminated area, not switching from a red lamp to a blue).
Thankyou! I was being careless and didn't read the original Post carefully.

Delta2 and jbriggs444
rsk
One of the biggest traps / most common errors in the levels I teach is when the question asks students to say what happens, in terms of number of electrons and ke of electrons (i) if intensity is increased keeping frequency the same (usually well answered) and (ii) if the frequency is increased keeping intensity the same (far more poorly answered).

Steve4Physics and Delta2