The anode voltage of a photocell is kept fixed. The wavelength lambda of the light falling on the ca

Q: Why doesn't the current increase when wavelength decreases?

Decreasing the wavelength increases the kinetic energy of the emitted electrons, but it doesn't change the number of electrons emitted per second. The current depends only on the number of electrons, which is determined by the intensity of the light.

Q: Doesn't option (a) show that current is independent of wavelength?

Yes, option (a) shows independence, but it implies the current is constant for all wavelengths. In reality, the current must drop to zero once the wavelength exceeds the threshold wavelength $\lambda_0$.

Q: What if the intensity was changing along with the wavelength?

If intensity changes, the current would change proportionally. However, in standard photoelectric experiments, when we say 'wavelength is gradually changed', we assume the intensity (energy per unit area per unit time) or the photon flux is kept constant.

Q: Why is the drop at $\lambda_0$ sudden and not gradual?

The photoelectric effect is a quantum phenomenon. A single photon must have enough energy to eject an electron. If its energy is even slightly below the work function (i.e., $\lambda > \lambda_0$), it cannot eject an electron, no matter how many such photons hit the surface. Hence, the drop is abrupt.

Q: Could the graph be a curve if we consider the energy distribution of photons?

If the light source is not perfectly monochromatic, there might be a slight curve near the threshold. But for a theoretical monochromatic source, it's a sharp step function.

Question

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows

Options:

(A)

(B)

(C)

(D) None of these

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine you are conducting a photoelectric experiment. You have a photocell, and you are shining light on its cathode.

The anode voltage is kept fixed, meaning we are not changing the potential difference that pulls the electrons.

We are gradually changing the wavelength $\lambda$ of the incident light. The question asks how the photoelectric current $I$ will respond to this change.

### The Master Equation

To understand this, we need to recall what actually causes the photoelectric current. The current $I$ is directly proportional to the number of photoelectrons emitted per second.

The number of emitted electrons depends entirely on the **intensity** of the incident light, which is the number of photons striking the surface per second.

As long as the intensity is constant, the current remains constant. Changing the wavelength $\lambda$ changes the kinetic energy of the emitted electrons, but it does not change their quantity.

### The Threshold Catch

However, there is a critical condition for emission to happen at all. The incident light must have enough energy to overcome the work function of the metal.

This means the wavelength $\lambda$ must be less than or equal to a specific threshold wavelength $\lambda_0$.

If $\lambda > \lambda_0$, the photons simply do not have enough energy to eject an electron. In this case, the emission stops completely, and the current $I$ drops to exactly zero.

### Graphing the Reality

So, what should the true graph of $I$ versus $\lambda$ look like?

For all wavelengths from zero up to $\lambda_0$, the current $I$ will be a constant, non-zero value. This part of the graph is a perfectly horizontal line.

But the moment $\lambda$ exceeds $\lambda_0$, the current abruptly falls to zero and stays there for all higher wavelengths. It is a step function!

### Evaluating the Options

Now let's look at the given options.

Option (a) shows a horizontal line that continues forever. This implies emission happens at all wavelengths, which violates the threshold condition.

Options (b) and (c) show the current varying continuously with wavelength, which contradicts the fact that current depends only on intensity.

Since none of the graphs correctly depict the sudden drop to zero at $\lambda_0$, the correct choice is **(d) None of these**.

Animated Solution for Physics - Dual Nature of Matter and Radiation: The anode voltage of a photocell is kept fixed. The wavelength $λ$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows

Select Answer:

Visualized Solution

$I$ vs $λ$ Graph

Threshold Condition

Current for $λ \leq λ_{0}$

Current for $λ > λ_{0}$

Evaluating Options

The Sigma Insight: Photoelectric Effect

Analyzing the Setup

The Master Equation

The Threshold Catch

Graphing the Reality

Evaluating the Options

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