Statement I: When ultraviolet light is incident on a photocell, its stopping potential is V0 and the

Q: Why does stopping potential increase with frequency?

Higher frequency means higher photon energy. This leads to a higher maximum kinetic energy of the emitted electrons, which in turn requires a larger negative potential (stopping potential) to stop them.

Q: Does the intensity of light affect the maximum kinetic energy?

No, intensity only affects the number of photoelectrons emitted per second. The maximum kinetic energy depends solely on the frequency of the incident light and the material's work function.

Q: Why do electrons have different kinetic energies if they absorb the same photon energy?

Electrons at different depths inside the metal lose varying amounts of energy through collisions with other atoms and electrons before escaping. This results in a spread of kinetic energies from zero to $K_{\text{max}}$.

Q: What exactly is monochromatic light?

Monochromatic light is light that consists of a single frequency or wavelength. Even with monochromatic light, the emitted electrons will have a range of kinetic energies due to internal collisions.

Q: Can an electron be emitted with zero kinetic energy?

Yes! If an electron loses an amount of energy during internal collisions that exactly equals the difference between the absorbed photon energy and the work function, it will emerge with zero kinetic energy.

Question

Statement I When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{	ext{max}}$. When the ultraviolet light is replaced by X-rays, both $V_0$ and $K_{	ext{max}}$ increase.
Statement II Photoelectrons are emitted with speeds ranging from zero to a maximum value, because of the range of frequencies present in the incident light.

Options:

(A) Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I

(B) Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I

(C) Statement I is true, Statement II is false

(D) Statement I is fase, Statement II is true

Sigma Percentile · Accepted Answer

### The Photoelectric Equation

To understand the photoelectric effect, we must start with Einstein's famous equation: $K_{	ext{max}} = h
u - \phi$. This elegant formula tells us that the maximum kinetic energy ($K_{	ext{max}}$) of an emitted electron depends directly on the frequency ($
u$) of the incident light and the work function ($\phi$) of the metal.

When we evaluate Statement I, we need to compare ultraviolet (UV) light with X-rays. From the electromagnetic spectrum, we know that X-rays possess a significantly higher frequency than UV light.

### Comparing UV and X-rays

Because the frequency of X-rays is higher ($
u_{	ext{X-ray}} > 
u_{	ext{UV}}$), the energy of the incident X-ray photons is also much greater. According to our master equation, this increase in photon energy directly translates to a higher maximum kinetic energy for the emitted electrons.

Furthermore, the stopping potential ($V_0$) is the electrical potential required to halt even the most energetic electrons. It is given by the relation $V_0 = \frac{K_{	ext{max}}}{e}$. Since $K_{	ext{max}}$ increases, the stopping potential $V_0$ must also increase. Therefore, Statement I is absolutely true!

### The Mystery of Varying Speeds

Now, let's dive into Statement II, which claims that the range of electron speeds is due to a range of frequencies in the incident light. Is this the real physical reason?

Imagine you are standing deep inside a crowded room (the metal) and someone hands you a burst of energy (the photon). To escape the room, you have to run toward the door (the surface). Even if everyone in the room receives the exact same amount of energy (monochromatic light), people starting from different depths will bump into others along the way.

These internal collisions cause the electrons to lose varying amounts of energy before they even reach the surface.

### Conclusion

Because of these collisions, electrons emerge with kinetic energies ranging from zero all the way up to the theoretical maximum ($K_{	ext{max}}$). The variation in speed is a direct result of internal collisions, not because the incident light had a range of frequencies.

Thus, Statement II is fundamentally flawed. Statement I is true, and Statement II is false, making option (c) the correct choice.

Select Answer:

Visualized Solution

$Analyzing Statement I$

$Frequency Comparison$

$Effect on K_{max} and V_{0}$

$Analyzing Statement II$

$Internal Collisions$

$Conclusion$

The Sigma Insight: Photoelectric Effect

The Photoelectric Equation

Comparing UV and X-rays

The Mystery of Varying Speeds

Conclusion

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