Number of photoelectrons liberated

In summary, the conversation discusses the calculation of the number of photoelectrons liberated from a metallic surface when a beam of light with two wavelengths and a total intensity of I is incident on it. It is assumed that there is no loss of light by reflection and each photon has enough energy to eject one electron. The number of photoelectrons emitted is found to be dependent on the wavelength of the incident light, as shown by the spectral response of some alkali photocathodes. This is due to the wavelength-dependence in the probability of photoemission.
  • #1
erisedk
374
7

Homework Statement


A beam of light has two wavelengths λ1 (A°, i.e. angstrom) and λ2 with total intensity of I (W/m2) equally distributed amongst the two wavelengths. The beam falls normally on an area A m2 of a clean metallic surface of work function φ (eV). Assume that there is no loss of light by reflection and that each photon has enough energy to eject one electron. Calculate the number of photoelectrons liberated in 2 seconds.

Homework Equations


E = nhc/λ

The Attempt at a Solution


Number of electrons liberated due to light of wavelength λ1 :
I/2×A×2 = n1 hc/λ1
n1 = ( IAλ1 )/hc
Similarly, n2 = ( IAλ2 )/hc
And answer will be n1 + n2
Which is indeed correct.
However, I don't understand something.
Shouldn't the number of photoelectrons ejected be independent of the wavelength of incident light (cos here n ∝ λ)? Isn't that what we've always heard, that number of photoelectrons ejected is only dependent on the intensity of incident light, as long as the light has enough energy to supersede the work function?
 
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  • #2
Silly problem. First of all because metallic surfaces are quite reflective (up to their plasma frequency).

And of course there is also a wavelength-dependence in the probability of photoemission.
 
  • #3
PietKuip said:
And of course there is also a wavelength-dependence in the probability of photoemission.

From what I know, the photoelectric current (or the number of photoelectrons emitted) only depends on the intensity of the incident light. Changing the frequency (or wavelength) of the incident light does not change the photoelectric current, as long as the frequency of the incident light is above the threshold frequency.
In this problem, number of photoelectrons emitted is dependent on the wavelength of the incident light. What part of my argument is wrong?
 
  • #4
erisedk said:
From what I know, the photoelectric current (or the number of photoelectrons emitted) only depends on the intensity of the incident light. Changing the frequency (or wavelength) of the incident light does not change the photoelectric current, as long as the frequency of the incident light is above the threshold frequency.
Of course the photoelectric current must depend on the color of the light. X-rays go straight through.
Here is a plot of the spectral response of some alkali photocathodes (note the logarithmic scale):
http://psec.uchicago.edu/library/photocathodes/zeke_Bialkali.png

The best these optimized materials can do is a quantum efficiency of about 25 % in the blue part of the spectrum.
 
Last edited:
  • #5
Thank you! I get it now. I was confusing and overcomplicating some things relating to saturation currents for different frequencies.
 
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Likes PietKuip

1. What is the definition of "number of photoelectrons liberated"?

The number of photoelectrons liberated refers to the number of electrons that are emitted from a material when it is exposed to light of a specific wavelength and intensity.

2. How is the number of photoelectrons liberated affected by the intensity of light?

The number of photoelectrons liberated is directly proportional to the intensity of light. This means that as the intensity of light increases, the number of photoelectrons liberated also increases.

3. How does the wavelength of light affect the number of photoelectrons liberated?

The number of photoelectrons liberated is inversely proportional to the wavelength of light. This means that as the wavelength of light decreases, the number of photoelectrons liberated increases.

4. What factors can influence the number of photoelectrons liberated?

The number of photoelectrons liberated can be influenced by factors such as the type of material, the intensity and wavelength of light, and the surface area of the material.

5. How is the number of photoelectrons liberated measured in experiments?

In experiments, the number of photoelectrons liberated can be measured using a device called a photomultiplier tube. This device detects and counts the number of photoelectrons emitted from a material when it is exposed to light.

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