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Franck-Hertz Experiment: Verification of Discrete Energy Levels

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Bohr Model of the Hydrogen AtomEnergy Levels of the Hydrogen Atom+1 more→→Stark Effect: Energy Level Splitting in Electric FieldsZeeman Effect: Magnetic Field Splitting of Energy Levels
atomic-physics energy-levels experimental-verification

Core Idea

In the Franck-Hertz experiment, electrons collide with atoms and can transfer energy. Below a threshold voltage, collisions are elastic. Once the collision energy exceeds the energy gap to the first excited state (~4.9 V for mercury), inelastic collisions occur: the electron loses energy in discrete quanta, and the atom is excited. This produces a sharp discontinuity in the current-voltage curve, directly confirming quantized energy levels.

How It's Best Learned

Plot current vs. voltage data from a Franck-Hertz tube, identifying the characteristic dips where inelastic collisions dominate. Calculate the excitation energy from the voltage at the first dip. Observe the repetition of dips at multiples of the first excitation voltage.

Common Misconceptions

Atoms can only absorb specific energies (the energy gaps between levels). Below-threshold collisions are elastic and don't excite the atom. The current drops where inelastic collisions dominate because fewer electrons have sufficient energy to reach the anode.

Explainer

From the Bohr model and hydrogen energy levels, you have a theoretical framework: electrons occupy discrete shells with specific energies, and transitions between levels involve photons with precisely quantized energies matching the energy gaps. This framework was built from spectroscopic data — the observation that atoms emit and absorb light only at specific wavelengths. The Franck-Hertz experiment (1914) provided something more direct: a purely mechanical, electrical demonstration that atomic energy levels are discrete, with no reference to light at all.

The experimental setup is deceptively simple. Electrons are emitted from a heated cathode, accelerated through mercury vapor by a voltage V, and collected at an anode (with a small retarding voltage opposing final collection). As V increases from zero, you might expect current to rise monotonically — more voltage, more electron energy, more electrons reaching the detector. Instead, the current-voltage curve shows a series of sharp *dips* at regular intervals of about 4.9 V. This periodic structure is the direct signature of a discrete energy level.

The mechanism operates through two kinds of collisions. For most of their journey, electrons undergo elastic collisions with mercury atoms: the electron bounces without transferring meaningful energy (the mercury atom is ~500 times heavier, so the electron barely slows, just like a tennis ball bouncing off a bowling ball). Electrons accumulate kinetic energy as they're accelerated. But once an electron's kinetic energy reaches exactly 4.9 eV — the energy separation between mercury's ground state and its first excited state — it can undergo an inelastic collision: it transfers exactly 4.9 eV to the mercury atom, dropping to near-zero kinetic energy itself. This nearly stopped electron cannot overcome the retarding voltage and reach the anode — current drops sharply. At slightly higher accelerating voltage, electrons reach the excitation threshold earlier in their path, then have room to reaccelerate and arrive at the anode — current rises again. At 9.8 V, an electron can undergo two sequential inelastic collisions, losing 4.9 eV each time, and current dips again. The dips at 4.9 V, 9.8 V, 13.7 V... directly count 1, 2, 3 excitation events per electron.

The crucial insight is the *sharpness* of the threshold. An electron with 4.85 eV cannot excite mercury's first state (which requires 4.9 eV); the collision is elastic. An electron with 4.95 eV can transfer exactly 4.9 eV and loses the remainder as kinetic energy. Atoms cannot accept arbitrary fractions of the excitation energy — they require the exact quantum. This all-or-nothing behavior is direct experimental evidence that atomic energy levels are discrete, not continuous. The Franck-Hertz experiment was decisive precisely because it bypassed optics entirely: no spectral lines, no prisms, no photographic plates — just a simple electrical measurement that forced the same conclusion as the entire history of atomic spectroscopy.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → Quantum Entanglement → Bell Theorem and Bell Inequalities → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → The WKB Approximation → WKB Quantization and Bohr-Sommerfeld Rule → Angular Momentum Quantization → Solution of the Hydrogen Atom → Introduction to Scattering Theory → Partial Wave Analysis in Scattering → Spin Angular Momentum → Electron Spin and Intrinsic Magnetic Moment → Stern-Gerlach Experiment: Spin Quantization and Measurement → Electron Diffraction and Matter Wave Properties → Davisson-Germer Experiment: Crystal Diffraction of Electrons → Electron Diffraction and Matter Wave Interference → Wavefunctions and Probability Density Interpretation → Quantum Superposition and Linear Combinations of States → Quantum Operators and Observables → Expectation Values and Averages → Time-Independent Perturbation Theory → Degenerate Perturbation Theory → Time-Dependent Perturbation Theory → Transition Probabilities and Selection Rules → Hydrogen Atom Spectral Series → Fine Structure and Relativistic Corrections → Energy Levels of the Hydrogen Atom → Franck-Hertz Experiment: Verification of Discrete Energy Levels

Longest path: 174 steps · 973 total prerequisite topics

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