How Does Stopping Potential Affect the Photoelectric Effect?
The photoelectric effect and stopping potential are key concepts in the study of modern physics and are frequently tested in examinations such as JEE Main. The photoelectric effect demonstrates the particle nature of light, relating the emission of electrons from a metal surface to the energy of incident photons. Stopping potential is used to quantitatively analyze this effect, directly connecting experimental observations to quantum theory.
Concept of Photoelectric Effect and Stopping Potential
The photoelectric effect refers to the emission of electrons from a metal surface when it is exposed to electromagnetic radiation of sufficient frequency. The ejected electrons are called photoelectrons, and their release depends on the energy of the incident photons surpassing the metal's work function. The stopping potential is the minimum negative potential applied to the collector plate, which just stops the most energetic photoelectrons from reaching the collector, resulting in zero photocurrent.
The effect highlights that electron emission occurs only if the frequency of incident radiation exceeds a certain threshold value, characteristic of the metal used. This threshold frequency determines whether photoelectrons are emitted, regardless of the intensity of light.
A detailed explanation of the photoelectric process, including experimental evidence, can be found in the provided Understanding Photoelectric Effect.
Einstein’s Equation and Stopping Potential Formula
Einstein explained the photoelectric effect using quantum theory, proposing that electromagnetic radiation consists of photons with discrete energy packets. The energy per photon is given by $E = h\nu$, where $h$ is Planck’s constant and $\nu$ is the frequency of light.
If the energy of an incident photon is greater than the work function ($\phi$) of the metal, an electron can be emitted with kinetic energy equal to the difference. The energy balance is expressed as:
$K_{\text{max}} = h\nu - \phi$
The maximum kinetic energy of photoelectrons is measured as the work done by the stopping potential ($V_0$) in bringing them to rest:
$eV_0 = h\nu - \phi$
This equation links stopping potential to the frequency of the incident light and the work function of the material.
For incident light of wavelength $\lambda$, the formula is written as:
$eV_0 = \dfrac{hc}{\lambda} - \phi$
Key variables in these equations are explained in the following table:
| Symbol | Quantity (SI Unit) |
|---|---|
| $h$ | Planck’s constant (J·s) |
| $\nu$ | Frequency (Hz) |
| $\lambda$ | Wavelength (m) |
| $e$ | Elementary charge (C) |
| $\phi$ | Work function (J) |
| $V_0$ | Stopping potential (V) |
Graphical Representation: Stopping Potential vs Frequency
The relationship between stopping potential ($V_0$) and frequency ($\nu$) is linear. This can be seen by rearranging Einstein’s equation for stopping potential as:
$V_0 = \dfrac{h}{e}\nu - \dfrac{\phi}{e}$
On a $V_0$ versus $\nu$ graph, the slope equals $\dfrac{h}{e}$ and the negative intercept on the $V_0$ axis corresponds to $-\dfrac{\phi}{e}$. No electrons are emitted for frequencies below the threshold frequency. As the frequency increases above this threshold, the stopping potential increases linearly.
The x-intercept of the graph indicates the threshold frequency, where the stopping potential becomes zero. The y-intercept gives information about the work function of the metal. The linear nature of this graph supports the photon theory of light, as established in modern physics and shown in Wave-Particle Duality Explained.
Experimental Setup and Determination of Stopping Potential
The classic setup to demonstrate the photoelectric effect consists of a vacuum tube with a photosensitive metal plate as the emitter and a collector electrode. Monochromatic light is incident on the metal surface, releasing photoelectrons. A variable voltage is applied between the collector and emitter. By increasing the negative potential at the collector, the kinetic energy of the arriving photoelectrons decreases.
The stopping potential is reached when the current due to photoelectrons drops to zero. At this voltage, even the most energetic photoelectrons are unable to reach the collector plate. This process is critical in verifying Einstein’s equation for the photoelectric effect and for measuring Planck’s constant experimentally. The method is often included in JEE and board-level experimental questions, as discussed in the Overview of Atomic Structure.
Key Factors Influencing Stopping Potential
Several physical quantities affect the stopping potential in the photoelectric effect. The main factors and their influence are summarized below:
| Factor | Effect on Stopping Potential |
|---|---|
| Frequency ($\nu$) of light | Directly proportional increase |
| Wavelength ($\lambda$) of light | Shorter $\lambda$ increases $V_0$ |
| Work function ($\phi$) | Higher $\phi$ lowers $V_0$ |
| Intensity of incident light | No effect on $V_0$ |
Intensity of light increases the number of emitted photoelectrons and thus the photocurrent, but does not affect their maximum kinetic energy or the stopping potential. Only the frequency of light and the specific work function of the metal surface determine the value of the stopping potential for a given experiment.
For further exploration of electromagnetic waves and their properties, refer to Electromagnetic Waves Overview.
Application and Use of Stopping Potential
Measurement of stopping potential enables the calculation of Planck’s constant from experimental data. By plotting stopping potential against the frequency of incident light for a given metal, the slope directly gives the ratio $h/e$. This method confirms the quantum theory of light.
The concept is used in various technological applications such as photoelectric cells and light sensors. The choice of metal for photoemissive surfaces depends on the desired work function and the operating wavelength range.
Knowledge of stopping potential is also crucial for understanding the working of devices in nuclear physics contexts, further explored in How Nuclear Reactors Work.
Typical Mistakes and Exam Guidance
In JEE Main examinations, it is essential to use SI units consistently. The work function is commonly given in electron volts (eV), but should be converted to joules when applying equations in SI units. Students must distinguish between the current versus voltage plot and the stopping potential versus frequency graph.
Threshold frequency is the lowest frequency at which the stopping potential becomes positive. For frequencies below this value, no emission occurs. These concepts frequently appear in multiple-choice and numerical problems in competitive exams.
A fundamental grasp of photon energy can be obtained from Understanding Photon Energy, which supports a deeper understanding of the photoelectric effect.
Summary Points on Photoelectric Effect and Stopping Potential
- Photoelectric emission occurs if frequency exceeds threshold
- Stopping potential blocks the most energetic photoelectrons
- Stopping potential depends on frequency, not intensity
- Shorter wavelength gives higher stopping potential
- Work function is material-dependent
- Linear $V_0$ vs $\nu$ plot allows $h$ calculation
- No photoemission occurs below threshold frequency
- Experimental setup validates Einstein’s equation
FAQs on What Is the Photoelectric Effect and Stopping Potential?
1. What is the photoelectric effect?
The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when exposed to light of sufficient frequency. Key aspects include:
- Emission occurs only if the incident light has a frequency above a certain threshold.
- The number of electrons emitted depends on the light's intensity.
- The kinetic energy of emitted electrons depends on the frequency, not the intensity, of the light.
2. What is stopping potential in the photoelectric effect?
Stopping potential is the minimum negative potential applied to a collector electrode in a photoelectric experiment to stop the most energetic photoelectrons from reaching it.
- It is denoted as V0.
- The value of stopping potential corresponds to the maximum kinetic energy of the emitted electrons.
- KEmax = eV0, where e is the charge of the electron.
3. What are the laws of photoelectric emission?
The laws of photoelectric emission describe how electrons are emitted from a metal surface under light illumination:
- Emission only occurs if the frequency of incident light is above a threshold value.
- The number of emitted electrons is proportional to the intensity of light (above threshold frequency).
- No time lag exists between light exposure and emission.
- The maximum kinetic energy of photoelectrons depends only on the frequency of the incident light, not on intensity.
4. How does intensity of light affect the photoelectric effect?
In the photoelectric effect, the intensity of light affects the number of emitted photoelectrons, but not their kinetic energy.
- Greater light intensity increases the number of photoelectrons released (current).
- Kinetic energy of the electrons remains constant for a given frequency, regardless of intensity.
5. What is the threshold frequency in the photoelectric effect?
Threshold frequency is the minimum frequency of incident light required to release electrons from a metal’s surface via the photoelectric effect.
- Denoted as f0 or ν0.
- Varies for different metals depending on their work function.
- No electrons are emitted if the light's frequency is below this value, regardless of its intensity.
6. What is Einstein’s photoelectric equation and how does it relate to stopping potential?
Einstein’s photoelectric equation mathematically describes the energy exchange in the photoelectric effect:
- K.E.max = hν – φ, where h is Planck’s constant, ν is the frequency, and φ is the work function.
- K.E.max = eV0, so eV0 = hν – φ
- Stopping potential (V0) can be used to find K.E.max of photoelectrons.
7. Why is there no photoemission below the threshold frequency?
Photoemission does not occur below threshold frequency because the energy of individual photons is insufficient to overcome the metal’s work function.
- Only photons with energy greater than the work function can release electrons.
- Photons of lower frequency do not have enough energy, regardless of intensity.
8. What factors affect the stopping potential in a photoelectric experiment?
The stopping potential in a photoelectric experiment is influenced by:
- The frequency of incident light: Higher frequencies result in higher stopping potentials due to greater electron kinetic energy.
- The nature of the metal, specifically its work function.
- The stopping potential is independent of light intensity.
9. State the significance of the photoelectric effect in physics.
The photoelectric effect is significant as it demonstrates the quantum nature of light and challenges the classical wave theory. It led to:
- Development of the photon theory of light.
- Introduction of the concept of quantized energy transfer.
- Confirmation of Einstein’s predictions, earning him the Nobel Prize in Physics.
- Applications in devices like photodiodes, solar cells, and night-vision equipment.
10. How does the stopping potential help determine the work function of a metal?
By measuring the stopping potential for various frequencies of incident light, the work function of a metal can be calculated using Einstein’s photoelectric equation.
- Plotting stopping potential versus frequency gives a straight line.
- The slope provides Planck’s constant; the intercept gives the metal’s work function.
- The relation eV0 = hν – φ is used for the calculations.
11. What experimental setup is used to study the photoelectric effect?
The photoelectric effect is studied using a vacuum tube containing a photoemissive cathode and a collector anode.
- Monochromatic light is shone on the cathode surface.
- Emitted electrons are collected by the anode, creating a current.
- A variable potential is applied to measure the stopping potential.
12. What are the applications of the photoelectric effect?
Applications of the photoelectric effect include:
- Photocells (light meters, automatic doors, and burglar alarms)
- Solar cells for energy conversion
- Television camera tubes
- Night-vision and optical sensors
- Study of material properties and quantum phenomena
