Stopping Potential vs Frequency in the Photoelectric Effect: Meaning, Graph, and Applications
Photoelectric Effect and Stopping Potential is a fundamental concept in modern physics, especially important for JEE Main. When light of suitable frequency falls on a metal surface, it can eject electrons instantly. This phenomenon is called the photoelectric effect, challenging classical wave theories of light.
To halt the fastest photoelectrons emitted from the surface, a reverse voltage must be applied. The minimum voltage required to just stop these electrons is termed the stopping potential. Its understanding is vital for interpreting experiments, as well as solving numericals that appear in JEE Main practice sets.
Understanding the Photoelectric Effect and Stopping Potential
The photoelectric effect shows that electron emission happens only if the incident light's frequency exceeds a certain threshold. The number and energy of emitted electrons depend on frequency and not just intensity. Photoelectric effect also explains key quantum principles.
The stopping potential acts as an energy barrier. It quantifies the maximum kinetic energy of photoelectrons and helps determine universal constants. Students should differentiate between stopping potential and work function for exam clarity.
- The higher the incident frequency, the more energy each photoelectron has.
- If frequency is below threshold, no electrons are emitted.
- Intensity increases electron number but not their kinetic energy or stopping potential.
- Experimental measurement of stopping potential validates Einstein's explanation.
- Practice problems often combine these points in JEE-style questions.
Einstein’s Equation and Formula for Stopping Potential
Einstein’s photoelectric equation links the incident light’s energy, the work function, and the kinetic energy of emitted electrons. Einstein’s photoelectric equation forms the theoretical backbone for photoelectric effect numericals.
The equation is:
E = hν = φ + Kmax,
where E is photon energy, h is Planck’s constant, ν is frequency, φ is work function, and Kmax is maximum kinetic energy.
The stopping potential (V0) is linked as:
Kmax = eV0
So,
eV0 = hν - φ
or
V0 = (h/e)ν - (φ/e)
where e is the charge of an electron.
| Symbol | Quantity | Unit (SI) |
|---|---|---|
| h | Planck’s constant | J·s |
| ν | Frequency of light | Hz |
| φ | Work function | J |
| e | Elementary charge | C |
| V0 | Stopping potential | V |
Graph of Stopping Potential vs Frequency
The graph of stopping potential versus frequency is linear, supporting quantum theory. The slope equals h/e. The intercept is connected to the material’s work function. Below threshold frequency, stopping potential is zero and no current is observed.
A typical JEE problem may involve determining Planck’s constant by plotting such a graph. Practicing these graphs builds intuition for the behavior of photoelectric current as you vary frequency.
- The x-intercept gives the threshold frequency.
- The y-intercept relates to work function (negative value).
- Slope is constant for all metals (Planck’s constant).
- Frequency increase shifts stopping potential higher.
Experimental Setup and Applications in JEE
A typical photoelectric experiment uses a vacuum tube, a photosensitive metal plate (cathode), a collector (anode), and an adjustable voltage source. Photoelectric effect and stopping potential are measured by adjusting the voltage until the current stops.
- Light of known frequency shines on the cathode.
- Emitted electrons travel to the anode, generating photocurrent.
- A reverse potential is steadily increased.
- The stopping potential is the voltage where current drops to zero.
Such an experiment is a direct method to verify quantum physics. The result matches Einstein's predictions, solidifying the quantum model over classical ideas.
Applications include studying energy bands, dual nature of matter, and determining fundamental constants.
Factors Affecting Stopping Potential
A key exam question is what influences stopping potential. Only frequency and the metal’s work function matter. Intensity and surface area do not change V0.
| Factor | Effect on Stopping Potential |
|---|---|
| Frequency (ν) | Directly proportional (increases V0) |
| Intensity | No effect |
| Work Function (φ) | Inverse (higher φ lowers V0) |
| Wavelength (λ) | Inverse relation (shorter λ, higher V0) |
Always recall that unlike the current, which depends on intensity, stopping potential depends only on photon's energy and work function. This highlights why classical predictions fail.
Numericals, Pitfalls, and JEE Preparation Tips
Below is a typical JEE Main example. Light of frequency 6.5×1014 Hz falls on a metal with work function 2.0 eV. Find stopping potential.
- Calculate photon energy: E = hν = 6.63×10-34 × 6.5×1014 = 4.31×10-19 J = 2.7 eV.
- Kinetic energy: Kmax = E - φ = 2.7 eV - 2.0 eV = 0.7 eV.
- Stopping potential V0 = Kmax/e = 0.7 V.
The final result is V0 = 0.7 V.
Common mistakes include using wrong units, confusing intensity with energy, or misinterpreting the work function symbol. Revise key formulas and always check units.
- Always use SI units throughout calculations.
- Work function φ given in eV must be converted to joules if needed.
- Current vs voltage plot is not the same as stopping potential graph.
- Threshold frequency is the lowest ν where V0 becomes positive.
- Practice with mock tests and practice papers on modern physics.
For recap, photoelectric effect and stopping potential directly connect quantum ideas to experiment. Stopping potential tests understanding of frequency, threshold, and work function concepts.
As you revise this chapter, focus on formula application and graphical reasoning. For more on exam strategies, see the JEE Main physics preparation tips from expert Vedantu faculty.
Mastering these basics will strengthen your grip on topics like electromagnetic waves and atomic structure too.
FAQs on Photoelectric Effect and Stopping Potential: Concept, Formula & Exam Guide
1. What is stopping potential in the photoelectric effect?
Stopping potential in the photoelectric effect is the minimum negative voltage applied to the collector plate that just prevents photoelectrons from reaching it, effectively stopping the photocurrent.
Key points:
- It is also called stopping voltage.
- Represents the maximum kinetic energy of emitted electrons in voltage units.
- Depends on the frequency of incident light and the work function of the metal.
2. What is the formula for stopping potential in photoelectric effect?
The stopping potential (V0) in the photoelectric effect is derived from Einstein’s equation and is given by:
- eV0 = hν - φ
- Where e is the charge of electron, h is Planck’s constant, ν (v) is frequency of incident light, and φ is the work function of the metal.
3. What is the relationship between wavelength and stopping potential in photoelectric effect?
The stopping potential is inversely related to the wavelength of incident light.
Explanation:
- Shorter wavelength (higher frequency) means more energy and a higher stopping potential.
- The relation: eV0 = hc/λ - φ
- As wavelength decreases, the stopping potential increases, provided intensity and metal remain the same.
4. Does stopping potential depend on the intensity of the incident light?
No, the stopping potential in the photoelectric effect does not depend on the intensity of the incident light.
Details:
- Changing intensity changes the number of photoelectrons (current) but not their maximum energy.
- Only the frequency of the light and the work function of the metal affect stopping potential.
5. How is stopping potential determined experimentally?
The stopping potential is found using a photoelectric cell by gradually applying a reverse (negative) voltage until the photoelectric current drops to zero.
Steps:
- Illuminate the metal surface with monochromatic light.
- Connect a variable voltage source with the negative terminal at the collector.
- Increase the negative voltage until the photoelectric current is just zero; this voltage is the stopping potential.
6. Why doesn’t the stopping potential change with light intensity?
The stopping potential is unaffected by the intensity of light because intensity changes the number of photons, not their energy.
Points to note:
- Photoelectron kinetic energy depends on the energy per photon (linked to frequency), not the number of photons.
- Intensity increase raises photocurrent but not the maximum kinetic energy or stopping potential.
7. What does the stopping potential in the context of the photoelectric effect depend on?
In the photoelectric effect, stopping potential depends on:
- The frequency of incident light (directly proportional)
- The work function of the metal (inverse relation)
8. How can stopping potential help determine Planck’s constant in experiments?
By plotting stopping potential (V0) versus frequency (ν) of incident light, the slope gives Planck’s constant (h/e).
Procedure:
- Measure stopping potential for different frequencies.
- Draw a V0 versus ν graph.
- The slope of the straight line is h/e, allowing calculation of h.
9. What is the difference between stopping potential and saturation potential?
Stopping potential and saturation potential are two distinct terms used in photoelectric effect experiments.
- Stopping potential: Minimum negative voltage to stop photoelectrons (zero current).
- Saturation potential: Voltage at which further increase no longer raises the photocurrent (all emitted electrons are collected).
10. Can stopping potential ever be zero? What does this imply?
Stopping potential can be zero only when the energy of incident photons equals the work function of the metal.
Meaning:
- When hν = φ, no photoelectrons have leftover kinetic energy.
- This occurs at threshold frequency; photoelectrons just barely escape.
- It indicates the minimum frequency required to emit electrons from the surface.
11. How does stopping potential vary with frequency in the photoelectric effect?
Stopping potential increases linearly with the frequency of incident light in the photoelectric effect.
Summary:
- Below threshold frequency, stopping potential is zero.
- For frequencies above threshold, higher frequency means greater stopping potential (higher kinetic energy).
- This linear relationship is often graphed and used to determine Planck’s constant.
12. Is stopping potential the same for all metals under the same light?
No, stopping potential depends on the work function of the metal, so different metals illuminated with the same frequency light will generally have different stopping potentials.
Key points:
- Metals with a higher work function require more energy, resulting in a lower stopping potential for the same frequency.
- This property is important for selecting materials in photoelectric experiments and devices.
