Stopping Potential (V₀) vs. Retarding Potential: Are They the Same?
Clearing up one of the most common confusions in Photoelectric Effect problems for JEE Physics.
🚨 The Short Answer
No, they are NOT the same! Stopping Potential is a specific value, while Retarding Potential is a general concept.
Stopping Potential (V₀) = The exact retarding potential that stops the most energetic photoelectrons
Why This Confusion Matters
This subtle distinction causes 65% of JEE aspirants to make errors in photoelectric effect problems. Understanding the difference can save you 2-3 crucial marks in your exam.
❌ Common Mistake in JEE
Students often write: $eV = h\nu - \phi$ for any retarding potential, when this equation is only valid for $V = V_0$ (Stopping Potential).
🎯 Quick Navigation
1. What is Retarding Potential?
The General Concept
Retarding Potential is any negative potential applied to the collector relative to the emitter that opposes the motion of photoelectrons.
💡 Simple Analogy
Think of retarding potential like a hill that electrons must climb. Any hill (potential) makes it harder, but only one specific height will stop them completely.
Effect on Photoelectrons
For a retarding potential $V$ (where $V < 0$), the energy equation becomes:
$$K.E._{\text{after}} = K.E._{\text{initial}} + eV$$
Since $V$ is negative, the final kinetic energy decreases.
✅ Key Characteristics
- General term for any opposing potential
- Can have any value from 0 to $V_0$ (negative scale)
- Reduces photocurrent but doesn't necessarily stop it
- Slows down photoelectrons but doesn't necessarily stop them
2. What is Stopping Potential (V₀)?
The Specific Value
Stopping Potential (V₀) is the minimum retarding potential required to stop the most energetic photoelectrons completely.
🎯 Critical Point
V₀ is not just "any" stopping potential - it's the exact value that makes photocurrent zero for the first time.
The Famous Equation
At stopping potential $V_0$, the maximum kinetic energy equals the potential energy:
$$eV_0 = K.E._{\text{max}} = h\nu - \phi$$
$$V_0 = \frac{h\nu - \phi}{e}$$
This equation is ONLY valid for $V = V_0$, not for any retarding potential!
✅ Key Characteristics
- Specific numerical value for given frequency
- Completely stops all photoelectrons
- Makes photocurrent zero
- Directly related to maximum kinetic energy: $eV_0 = K.E._{\text{max}}$
3. Side-by-Side Comparison
Retarding Potential vs Stopping Potential
| Aspect | Retarding Potential | Stopping Potential (V₀) |
|---|---|---|
| Definition | Any potential that opposes electron motion | Specific potential that stops most energetic electrons |
| Nature | General concept | Specific value |
| Values | 0 to V₀ (range) | One specific value |
| Effect on Current | Reduces photocurrent | Makes photocurrent zero |
| Energy Equation | $K.E._{\text{final}} = K.E._{\text{initial}} + eV$ | $eV_0 = K.E._{\text{max}} = h\nu - \phi$ |
| JEE Importance | Conceptual understanding | Numerical problems, graphs |
💡 Memory Trick
"All Stopping Potentials are Retarding Potentials, but not all Retarding Potentials are Stopping Potentials."
Just like: "All squares are rectangles, but not all rectangles are squares."
4. Common JEE Problem Types
Problem Type 1: Direct Calculation
Example Problem
Light of wavelength 200 nm falls on a metal surface with work function 4.2 eV. Calculate the stopping potential.
Solution:
Energy of photon: $E = \frac{hc}{\lambda} = \frac{1240 \text{ eV·nm}}{200 \text{ nm}} = 6.2 \text{ eV}$
Maximum K.E.: $K.E._{\text{max}} = E - \phi = 6.2 - 4.2 = 2.0 \text{ eV}$
Stopping potential: $eV_0 = K.E._{\text{max}} \Rightarrow V_0 = 2.0 \text{ V}$
Problem Type 2: Conceptual Understanding
Example Problem
If a retarding potential of 1.5 V is applied and photocurrent is still flowing, what can you conclude about the stopping potential?
Solution:
Since photocurrent is still flowing at V = -1.5 V, this means:
• The retarding potential (1.5 V) is less than the stopping potential
• Therefore, $V_0 > 1.5 \text{ V}$
• Some photoelectrons still have enough energy to reach the collector
🧠 Quick Self-Test
Q1: Can stopping potential be positive?
Q2: If photocurrent becomes zero at V = -2.3 V, what is V₀?
Q3: For a retarding potential of 1.8 V, can we write $e(1.8) = h\nu - \phi$?
Answers
A1: No, stopping potential is always negative (or zero) as it opposes electron motion
A2: V₀ = 2.3 V (magnitude only, the sign is understood to be negative)
A3: No! This equation is only valid for V = V₀ (stopping potential)
🎯 JEE Exam Tips
If question says "retarding potential", be careful about using $eV = h\nu - \phi$
Stopping potential is usually quoted as positive (V₀ = 2V means potential is -2V)
On I-V graphs, stopping potential is where curve hits V-axis
If problem gives numerical value for "potential", it's likely asking about stopping potential
🎉 Summary: Key Takeaway
Mastered This Concept?
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