# Wavelength-stopping potential dependence

• Krushnaraj Pandya
In summary, the conversation discusses the effect of changing the wavelength of a point source emitting light on the saturation current and stopping potential in a metallic cathode of a photoelectric cell. It is determined that while the number of electrons ejected remains the same, doubling the energy of a photon by halving the wavelength will result in a more than doubled stopping potential due to the relationship between energy and velocity of an electron. The relevant equation is given as hf=work function+eV, and it is concluded that doubling hf without changing the work function will result in a more than doubled eV.
Krushnaraj Pandya
Gold Member

## Homework Statement

Consider a point source emitting light of wavelength 5000 A. Light from this source is falling on a metallic cathode of photoelectric cell. It is also given that energy of a photon of wavelength 10,000 A is 1.23 eV. If the source of 5000 A is replaced by 2500 A wavelength but emitting same no. of photons in unit time, what will happen to the saturation current and stopping potential respectively?

## Homework Equations

eV=KE(max)
no. of electrons ejected=no. of photons colliding (energy above work function)

## The Attempt at a Solution

since no. of electrons ejected does not change with change in energy of photon, saturation photocurrent remains same.
halving the wavelength doubles the energy of a photon and therefore the electron, since V and energy of electron=0.5mv^2 are directly proportional. Stopping potential should be doubled, but the answer is given as it is more than doubled. Where am I wrong? I suspect doubling wavelength won't double the KE since work function is not zero- but then how do I arrive at the correct relation?
I'd appreciate some help, thank you

Where did you get your "relevant equation"? Isn't it missing something?

mjc123 said:
Where did you get your "relevant equation"? Isn't it missing something?
hf=work function+eV

So if you double hf without changing WF, how will eV change?

mjc123 said:
So if you double hf without changing WF, how will eV change?
Right, it will more than double

Thank you very much for your help :D

## 1. What is "wavelength-stopping potential dependence"?

"Wavelength-stopping potential dependence" refers to the relationship between the wavelength of light and the minimum potential required to stop the emission of photoelectrons from a metal surface. This phenomenon is explained by the photoelectric effect, which states that when light of a certain wavelength is shone on a metal surface, it can cause the emission of electrons.

## 2. How does the wavelength of light affect the stopping potential?

The shorter the wavelength of light, the higher the stopping potential required to stop the emission of photoelectrons. This is because shorter wavelengths have higher energy photons, which can cause the electrons to be ejected with more energy and require a higher potential to stop them.

## 3. What is the significance of the wavelength-stopping potential dependence?

The wavelength-stopping potential dependence is significant because it provides evidence for the particle nature of light. According to the photoelectric effect, light is made up of particles (photons) that can transfer their energy to electrons in a one-to-one interaction. This supports the idea of light as discrete energy packets rather than a continuous wave.

## 4. How is the wavelength-stopping potential dependence experimentally determined?

To determine the wavelength-stopping potential dependence, a metal surface is irradiated with light of varying wavelengths while the stopping potential is measured. The stopping potential is then plotted against the corresponding wavelengths to determine the relationship between them.

## 5. What factors can affect the wavelength-stopping potential dependence?

The wavelength-stopping potential dependence can be affected by the properties of the metal surface, such as its work function and surface roughness. It can also be affected by the intensity of the light, as higher intensity can increase the number of photons and therefore affect the stopping potential. Additionally, the accuracy of the measurement instruments and experimental conditions can also impact the results.

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