Question

In a photoelectric experiment a student uses a light source whose frequency is greater than that needed to eject electrons from a certain metal. However, after continuously shining the light on the same area of the metal for a long period of time the student notices that the maximum kinetic energy of ejected electrons begins to decrease, even though the frequency of the light is held constant. How would you account for this behavior?

Short answer

Surface changes, like oxidation, increase the work function, reducing electron kinetic energy.

Step-by-step solution

Understanding the Photoelectric Effect

The photoelectric effect involves electrons being ejected from a metal surface when it is exposed to light of sufficiently high frequency. The maximum kinetic energy of ejected electrons is given by \( KE_{max} = hf - ext{work function} \), where \( hf \) is the energy of the photons, and the work function is the minimum energy required to eject an electron.

Identifying the Key Factors

The frequency of light being constant means the energy \( hf \) of the incident photons remains unchanged. However, the decrease in the maximum kinetic energy of electrons suggests changes in the metal's surface properties impacting the work function.

Considering Surface Condition Changes

Over time, continuous illumination might cause the metal surface to undergo physical or chemical changes, such as oxidation or surface contamination. These changes possibly increase the work function of the metal.

Impact of Increased Work Function

An increase in the work function means that more energy is needed to eject an electron. Therefore, even though the frequency (and thus energy) of the light remains constant, the additional energy required due to an increased work function results in lower kinetic energy for the ejected electrons.

Conclusion

The decrease in the maximum kinetic energy of ejected electrons over time is likely due to increased work function from surface changes like oxidation or contamination during prolonged exposure to light.

Key concepts

Kinetic Energy

Kinetic energy in the context of the photoelectric effect refers to the energy that ejected electrons possess as they move away from the metal surface. When light shines on the metal, photons transfer their energy to electrons. This transfer allows electrons to break free from the metal's surface.

The maximum kinetic energy of an ejected electron is expressed by the equation \( KE_{max} = hf - \text{work function} \). Here, \( hf \) is the energy of the light (or photons) impacting the metal. This equation tells us how much energy an electron will have after escaping, provided the incoming light energy exceeds the work required to release it.

• If the light frequency is high, the energy \( hf \) is large, potentially leading to greater kinetic energy for the ejected electrons.
• If the light frequency is low, electrons might not be ejected at all.

Thus, kinetic energy of ejected electrons is directly tied to both the incoming light's frequency and the work function of the material.

Work Function

The work function is a pivotal concept in understanding electron ejection through the photoelectric effect. It is the minimum amount of energy needed to remove an electron from the surface of a metal. Each metal has a specific work function that depends on its atomic structure and surface properties.

The work function is essentially the energy barrier that confines electrons within the metal. For electrons to be ejected, the energy of incoming photons must first overcome this barrier. Only then can any excess energy turn into the kinetic energy of the ejected electrons.

• A higher work function means more energy is required for electron ejection.
• Factors like surface contamination can alter the work function, as contamination can modify surface properties.

Changes in the work function directly influence the kinetic energy of ejected electrons, demonstrating how strongly surface conditions affect this process.

Electron Ejection

Electron ejection is the core of the photoelectric effect, where electrons gain enough energy from absorbed photons to leave the metal surface. For electron ejection to occur, the energy of the incoming light must be greater than the metal's work function.

When electrons absorb adequate photon energy, they overcome the work function and gain kinetic energy, allowing them to escape. The photoelectric effect can be influenced by several factors:

• The frequency of the light, which determines the energy per photon and, if high enough, can facilitate electron ejection.
• The condition of the metal surface, including potential contamination or oxidization, which can impact the work function and hence the likelihood and characteristics of electron ejection.

Understanding electron ejection helps illustrate the relationship between photon energy and the material's surface characteristics in enabling the photoelectric effect.

Surface Contamination

Surface contamination refers to any foreign substance or material that builds up on the metal surface. This build-up can occur due to environmental exposure, chemical reactions, or prolonged interactions with light or other matter. Such contamination can significantly affect the metal's properties.

In the context of the photoelectric effect, surface contamination can increase the metal's work function, making it more difficult for electrons to escape. This happens because the contamination layers might create an additional energy barrier that electrons need to overcome. This is why, even with constant frequency (and thus constant energy of the incoming light), the kinetic energy of ejected electrons might decrease over time as contamination builds up.

• Surface changes can include oxidation or adsorbed molecules, altering the electron emission characteristics.
• Regularly cleaning the metal surface or carrying experiments in controlled conditions might help mitigate such effects.

This concept underlines the importance of maintaining pristine surface conditions during experiments to achieve accurate photoelectric effect observations.