What is the common error when discussing the photoelectric effect?

In summary, the conversation discusses the interdependence of intensity (I), frequency (f), and maximum kinetic energy (KE_max). The equation KE_max = IA/N - W is used to illustrate how changes in intensity and frequency can affect KE_max, with the assumption that frequency is being held constant. The conversation highlights the importance of considering both intensity and frequency when determining the relationship between KE_max and I.
  • #1
Aurora_b
4
3
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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  • #2
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?
 
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  • #3
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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  • #4
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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  • #5
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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Related to What is the common error when discussing the photoelectric effect?

1. What is the photoelectric effect problem?

The photoelectric effect problem refers to the phenomenon where light, when shone on certain materials, causes the emission of electrons from the surface of the material. This effect was first observed by Heinrich Hertz in 1887 and later explained by Albert Einstein in 1905.

2. What causes the photoelectric effect?

The photoelectric effect is caused by the interaction between photons (particles of light) and electrons in the material. When a photon with enough energy strikes the surface of the material, it can transfer its energy to an electron, causing it to be ejected from the material.

3. What is the significance of the photoelectric effect problem?

The photoelectric effect problem has significant implications in the fields of physics and technology. It provided evidence for the particle nature of light and helped develop the concept of photons. It also led to the development of technologies such as solar cells and photoelectric sensors.

4. What factors affect the photoelectric effect?

The photoelectric effect is affected by several factors, including the intensity of the incident light, the frequency (or color) of the light, and the material's properties. Higher intensity and shorter wavelengths of light can increase the number of electrons emitted, while certain materials have a lower threshold for the photoelectric effect to occur.

5. How is the photoelectric effect problem explained by quantum mechanics?

Quantum mechanics explains the photoelectric effect by treating light as both a wave and a particle. The energy of a photon is determined by its frequency, and only photons with enough energy can cause the photoelectric effect. This theory also explains the observation that the number of electrons emitted is directly proportional to the intensity of the light, as more photons with higher energy can cause more electrons to be ejected.

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