1: The Dawn of the Quantum Theory
- Page ID
- 11778
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)"A profound change has taken place during the present century in the opinions physicists have held on the mathematical foundations of their subject. Previously they supposed that the principles of Newtonian mechanics would provide the basis for the description of the whole of physical phenomenon and that all the theoretical physicists had to do was suitably to develop and apply these principles. With the recognition that there is no logical reason why Newtonian and classical principles should be valid outside the domains in which they have been experimentally verified has come the realization that departures from these principles are indeed necessary. Such departures find their expression through the introduction of new mathematical formalisms, new schemes of axioms and rules of manipulation, into the methods of theoretical physics." P. A. M. Dirac, "Quantum Mechanics" (1930).
- 1.1: Blackbody Radiation Cannot Be Explained Classically
- This page explores blackbody radiation, emphasizing its importance in physics and key laws such as Stefan-Boltzmann and Wien’s Displacement Law, which link emitted power and peak wavelength to temperature. It details historical contributions from scientists like Kirchhoff and discusses thermal radiation concepts, including the sun's output. The Rayleigh-Jeans Law's limitations are highlighted, notably the ultraviolet catastrophe, which arises from its failure at high frequencies.
- 1.2: Quantum Hypothesis Used for Blackbody Radiation Law
- This page discusses Max Planck's groundbreaking work on blackbody radiation, leading to the conclusion that energy is quantized, emitted in discrete amounts known as quanta. This idea resolved the ultraviolet catastrophe faced by classical physics and established the foundation for quantum theory.
- 1.3: Photoelectric Effect Explained with Quantum Hypothesis
- This page discusses the photoelectric effect, highlighting the threshold frequency for electron emission and its demonstration of light's dual wave-particle nature. Einstein’s quantum theory explains the relationship between light frequency and the energy of ejected electrons, while the work function represents the energy needed to remove an electron from a metal. Initial resistance to these ideas was later overcome by Millikan's confirmation.
- 1.4: The Hydrogen Atomic Spectrum
- This page covers the absorption and emission line spectra of hydrogen, focusing on the Balmer series as described by Johann Balmer. It mentions historical contributions from Isaac Newton, Anders Ångström, William Wollaston, and Joseph von Fraunhofer. The text details how line spectra reveal atomic structure and discusses the relationship between wavelength and frequency using wavenumbers.
- 1.5: The Rydberg Formula and the Hydrogen Atomic Spectrum
- This page discusses Rydberg's theory and Balmer's formula for predicting hydrogen spectrum wavelengths, highlighting Balmer's 1885 formula for visible wavelengths and Rydberg's generalization for all atomic spectra, including the Lyman series in the ultraviolet. The Lyman series corresponds to transitions to the n=1 orbit, with relevant formulas and values mentioned. Various sequentially named series are outlined, emphasizing that atomic spectra provide insights into atomic structure.
- 1.6: Matter Has Wavelike Properties
- This page explores the wave-particle duality of matter, particularly through de Broglie's 1924 Ph.D. thesis, which posits that particles like electrons exhibit wave-like properties linked to their momentum. His theory, originally met with skepticism, gained endorsement from Einstein and introduced the concept of the de Broglie wavelength.
- 1.7: de Broglie Waves can be Experimentally Observed
- This page explores wave-particle duality, illustrating how particles like electrons and neutrons can display wave-like properties, supported by phenomena like electron diffraction and the Young double-slit experiment. This duality is crucial to quantum mechanics and has practical implications in technologies like electron microscopes.
- 1.8: The Bohr Theory of the Hydrogen Atom
- This page examines Rutherford's atomic model's shortcomings, notably its inability to explain atomic stability. It then introduces the Bohr model, developed by Niels Bohr in 1913, which quantizes electron orbits within hydrogen, connecting quantum mechanics to atomic spectra. The page details Bohr's assumptions, the concept of the Bohr radius, and the Rydberg equation, alongside corrections for precise calculations.
- 1.9: The Heisenberg Uncertainty Principle
- This page explains the Heisenberg Uncertainty Principle, which asserts that the exact position and momentum of a particle cannot be measured simultaneously with precision. It discusses the implications for quantum mechanics, including wave-particle duality and the probabilistic nature of particles, as shown in experiments like the double-slit experiment.
- 1.E: The Dawn of the Quantum Theory (Exercises)
- This page explores various physics concepts, including the photoelectric effect, blackbody radiation, and quantum mechanics calculations. It addresses kinetic energies, photon interactions, and work functions for metals like sodium and gold. Topics such as the Paschen and Balmer series, de Broglie wavelengths, and the Heisenberg Uncertainty Principle are discussed, along with applicable equations and calculations.
Thumbnail: The Photoelectric effect require quantum mechanics to describe accurately (CC BY-SA-NC 3.0; anonymous via LibreTexts).