The anode voltage of a photocell is kept fixed. The wavelength ? of the light falling on the cathode is gradually changed. The plate current I of the photocell varies ? explain with graph ?

In a photocell, the interaction between light and the cathode leads to the emission of electrons, which generates a current. When the anode voltage is fixed and the wavelength of the incident light is varied, the behavior of the plate current can be understood through the principles of the photoelectric effect. Let's break this down step by step.

The Photoelectric Effect

The photoelectric effect occurs when light photons strike a material and provide enough energy to eject electrons from that material. The energy of a photon is given by the equation:

E = h * f

where E is the energy of the photon, h is Planck's constant, and f is the frequency of the light. Since frequency and wavelength are related by the equation c = λ * f (where c is the speed of light and λ is the wavelength), we can also express the energy in terms of wavelength:

E = h * c / λ

Impact of Wavelength on Plate Current

As the wavelength of the light falling on the cathode is gradually changed, the energy of the photons changes accordingly. Here's how this affects the plate current:

• Short Wavelength (High Energy): When the wavelength is short (or frequency is high), the photons have enough energy to eject electrons efficiently. This results in a higher plate current.
• Threshold Wavelength: There exists a specific wavelength (threshold wavelength) below which the energy of the photons is sufficient to overcome the work function of the material. Below this wavelength, electrons are emitted, and the current increases significantly.
• Long Wavelength (Low Energy): As the wavelength increases beyond the threshold, the energy of the photons decreases. Eventually, if the wavelength is too long, the photons will not have enough energy to eject electrons, and the plate current will drop to zero.

Graphical Representation

To visualize this relationship, we can plot a graph of plate current (I) against wavelength (λ). The graph would typically look like this:

• On the x-axis, we have the wavelength (λ).
• On the y-axis, we have the plate current (I).

The graph would show:

• A steep increase in current as the wavelength decreases to the threshold value.
• A plateau or gradual increase in current as the wavelength approaches the threshold.
• A sharp drop to zero current as the wavelength increases beyond the threshold.

Conclusion

In summary, the relationship between the wavelength of light and the plate current in a photocell is crucial for understanding the photoelectric effect. As the wavelength decreases, the energy of the photons increases, leading to a higher plate current until the threshold wavelength is reached. Beyond this point, the current ceases as the energy becomes insufficient to eject electrons. This phenomenon not only illustrates fundamental principles of physics but also has practical applications in various technologies, such as solar cells and photodetectors.