What is the common error when discussing the photoelectric effect?

AI Thread Summary
The discussion highlights a common misunderstanding regarding the relationship between intensity, frequency, and maximum kinetic energy (KE_max) in the photoelectric effect. It clarifies that while intensity is often thought to depend solely on the number of photons (N), it also depends on frequency (f). When intensity is increased by doubling frequency, KE_max increases; however, if intensity is increased without changing frequency, KE_max remains constant. The text emphasizes that the assumption of constant frequency is crucial when discussing the independence of KE_max from intensity. This misunderstanding is frequently encountered in educational settings, particularly when students analyze changes in electron behavior under varying conditions.
Aurora_b
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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.
f= frequency of incident radiation
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
f= frequency of incident radiation
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.
 
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Aurora_b said:
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?
 
Steve4Physics said:
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).
 
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jbriggs444 said:
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.
 
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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).
 
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