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Photoelectron Spectroscopy (PES)

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photoelectron spectroscopy binding energy subshells electron configuration evidence AP Chemistry

Core Idea

Photoelectron spectroscopy shines high-energy light on atoms, knocks out electrons, and measures their kinetic energy. The binding energy of each electron is the photon energy minus that kinetic energy. A PES spectrum shows one peak for each occupied subshell: the peak's position gives the binding energy, and its relative height gives the number of electrons in that subshell. PES therefore provides direct experimental evidence for shells, subshells and electron configurations.

How It's Best Learned

Start from a known configuration, such as neon's 1s² 2s² 2p⁶, and predict its spectrum before looking at it: three peaks, heights 2:2:6, with 1s far to the high-energy side. Then reverse the task and identify unknown elements from spectra. Finally, compare the same subshell across neighboring elements to see how nuclear charge shifts binding energy.

Common Misconceptions

Explainer

You have learned to write electron configurations like 1s² 2s² 2p⁶. Photoelectron spectroscopy is one of the experiments that shows these configurations are real.

The method builds on the photoelectric effect. A beam of photons with a known, high energy, usually X-rays or far ultraviolet light, strikes a sample of gaseous atoms. Each photon can eject one electron. The instrument measures the kinetic energy of the ejected electrons. Energy is conserved, so:

binding energy = photon energy − kinetic energy

Electrons held loosely leave with a lot of kinetic energy and have a small binding energy. Electrons held tightly leave with little kinetic energy and have a large binding energy.

A PES spectrum plots the number of electrons detected against binding energy. Electrons from the same subshell all have about the same binding energy, so they appear together as one peak. Two features of each peak carry information. Its position tells you how tightly those electrons are held. Its relative height tells you how many electrons are in that subshell.

Consider neon. Its spectrum has three peaks, at about 84, 4.7 and 2.1 MJ/mol. The first is the 1s subshell, deep in the atom and close to the nucleus. The other two are 2s and 2p. Their heights are in the ratio 2 : 2 : 6, matching the configuration exactly. Notice that the lowest binding energy, about 2.1 MJ/mol, equals neon's first ionization energy.

The spectrum also shows things that a configuration alone does not. The 2s and 2p peaks are separate, so electrons in the same shell can have different energies. Moving from one element to the next, the same subshell shifts to higher binding energy because the nucleus has one more proton. Sodium's 1s peak lies at higher energy than neon's, and sodium adds a small fourth peak for its single 3s electron at a very low binding energy.

The same principle, applied with X-rays to solid surfaces, is X-ray photoelectron spectroscopy (XPS), a standard tool for finding which elements are present at a surface and in what oxidation states. Kai Siegbahn shared the 1981 Nobel Prize in Physics for developing high-resolution electron spectroscopy.

Practice Questions 4 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 → Combining Small Groups Within 5 → Number Bonds Within 5 → Number Bonds to 10 → Tens and Ones Place Value → Reading and Writing Three-Digit Numbers → Comparing Three-Digit Numbers → Comparing and Ordering Three-Digit Quantities → Comparing and Ordering Whole Numbers → Comparing Numbers 1 to 20 → Ordering Numbers to 20 → Number Line 0 to 20 → 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 → Opposites and Additive Inverses → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Multiplying Binomials (FOIL) → Factoring Trinomials → Factoring Completely → Introduction to Rational Expressions → Simplifying Radical Expressions → Segments and Distance → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Similar Right Triangles and the Geometric Mean → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Special Right Triangles: 30-60-90 → 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 → Green's Theorem and Its Applications → Divergence Theorem: Flux and Outflow → 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 → Parallel Plate Capacitor Geometry and Field → 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 → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Ionization Energy → Photoelectron Spectroscopy (PES)

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