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What is the slope of the graph plotting Stopping Potential (V₀) against incident frequency (ν)?

h / e. From eV₀ = hν - Φ₀ ⇒ V₀ = (h/e)ν - (Φ₀/e). Comparing to y = mx + c, the slope is h/e (a universal constant).

Physics · Class 12 · JEE / NEET / AP Physics

Dual Nature of Radiation & Photoelectric Effect

ThePhotoelectric Effectestablished the particle nature of light. Photons transfer their discrete quanta of energy $E = h\nu$ to metal conduction electrons in an instantaneous one-to-one collision, ejecting photoelectrons.

11. Visual Overview & Intuitive Discovery: Dual Nature of Radiation & Photoelectric Effect

Albert Einstein is universally famous for his theory of relativity and $E = mc^2$ . Yet his 1921 Nobel Prize in Physics was NOT awarded for relativity—it was awarded for his explanation of the Photoelectric Effect! By showing that light exists as discrete quantum energy bullets called photons, Einstein launched the quantum revolution that gave birth to lasers, solar panels, and digital cameras.

Photoelectric Effect & Stopping Potential Curve: Einstein's Equation, Work Function (Φ₀), Stopping Potential (V₀), De Broglie Hypothesis — Photoelectric Effect & Stopping Potential Curve
Incoming photon colliding with metal surface electron and linear stopping potential V₀ vs frequency ν graph with slope h/e.
1Einstein's Equation — hν = Φ₀ + K_max = hν₀ + e V₀
2Work Function (Φ₀) — Minimum energy needed to liberate an electron from the metal surface
3Stopping Potential (V₀) — Negative anode potential required to stop the fastest electron: e V₀ = K_max
4De Broglie Hypothesis — λ = h / p = h / √(2mE), particles possess wave properties

Interactive Study Prompts (Click to Explore)

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AI Deep Dive 🪄

22. Physical Mechanism Flowchart: Dual Nature of Radiation & Photoelectric Effect

Dual Nature of Radiation & Photoelectric Effect Step-by-Step Flowchart

1
Initial State
Initial parameters and boundary conditions are established.
2
Fundamental Force/Interaction
Governing physical laws act continuously across the system.
3
Energy & Vector Conservation
Conservation principles restrict permitted trajectory states.
4
Dynamic Equilibrium
Final observable state satisfies equilibrium equations.

Follow the numbered pipeline above. In physics examinations, sketching this mental flowchart ensures you never miss intermediate steps in complex multi-concept numericals.

33. Rigorous Mathematical Proofs & Governing Equations

Derivation — Derivation of Governing Formula for Dual Nature of Radiation & Photoelectric Effect

1
$F_{\text{net}} = m a$
Starting from Newton's foundational law
2
$\int F \, dx = \Delta K$
Integrating over displacement

Fundamental Relation

E = m c^2

Core Physical Variables

Variable	Symbol	SI Unit
Energy	E	Joules (J)
Power	P	Watts (W)

Energy
Symbol
E
SI Unit
Joules (J)
Power
Symbol
P
SI Unit
Watts (W)

44. Green Energy: The Physics of Photovoltaic Solar Panels

Every rooftop solar panel in the world is a quantum photoelectric device. When sunlight photons with energy greater than the bandgap ( $h\nu > E_g$ ) strike silicon atoms, they liberate valence electrons into the conduction band via photoelectric absorption. An internal P-N junction electric field sweeps these liberated electrons across the junction, generating clean, renewable electrical current from pure sunshine.

Common mistake: Misconception: "Increasing the brightness (intensity) of light will make the emitted photoelectrons fly out with higher speed." Intensity represents photon flux (photons per second), not energy per photon! Increasing intensity increases only the NUMBER of photoelectrons emitted per second. The maximum kinetic energy and speed of electrons depends exclusively on the frequency/color of the incident light (

K_{\text{max}} = h\nu - \Phi_0

55. Solved Standard & Advanced Exam Problems

Exam question · JEE Standard

Sample Question

Exam question · JEE Main & NEET

When light of frequency 2ν₀ (where ν₀ is the threshold frequency) strikes a metal surface, the maximum velocity of photoelectrons is v₁. When the frequency is increased to 5ν₀, the maximum velocity is v₂. What is the ratio v₁ / v₂?

A.1 : 2
B.1 : 4
C.1 : √2
D.2 : 5

Remember

Photoelectric emission is an instantaneous process (< 10⁻⁹ s) without time lag.
Maximum kinetic energy of photoelectrons depends strictly on incident frequency, not intensity.
Number of photoelectrons emitted per second (photocurrent) is directly proportional to incident light intensity.

Check yourself

Question 1
What is the slope of the graph plotting Stopping Potential (V₀) against incident frequency (ν)?