Typical electron diffraction pattern obtained in a TEM with a parallel electron beam

Typical electron diffraction pattern obtained in a transmission electron microscope with a parallel electron beam.

Modern physics encompasses the twentieth century developments in science that arose from measurements using modern instrumentation showing that nineteenth century, or 'classical' descriptions of nature were not sufficient. The most significant developments were Einstein's general relativity, quantum theory and high energy particle physics. For the most part, relativity and high energy particle physics are not going to be tested on the MCAT, except insofar as a general, superficial sense of those subjects can help contextualize certain aspects of basic nuclear physics or atomic theory. Quantum theory is different. A good sense of the most important discoveries is an essential foundation for general chemistry. There is a lot of overlap between this chapter on Modern Physics and our chemistry chapter, Atomic Theory. While many classical approaches, such as for basic modeling of electrostatic potential energy changes, can be extremely helpful to building intuition for general chemistry, you must keep quantum theory always present to mind because without it there is no way to understand the structure of matter at the atomic and molecular level.

WikiPremed Resources

Modern Physics Cards
Chapter from the Wisebridge Learning System for Physics

Modern Physics Images
Image gallery for study with links to larger teaching JPEGs for classroom presentation

Question Drill for Modern Physics
Conceptual Vocabulary Self-Test

Basic Terms Crossword Puzzle

Basic Puzzle Solution

Learning Goals


Understand what blackbody radiation is and be able to describe the significance of Planck's solution to the problem of how to interpret blackbody radiation curves versus classical theory.

Be able to describe the relationship between the frequency of electromagnetic waves and photon energy and feel comfortable applying the quantization of light energy to interpreting a range of phenomena such as atomic emission spectra or the photoelectric effect.

Be ready to solve problems involving the basic apparatus for demonstrating the photoelectric effect and interpret results to determine the work function.

Possess a basic familiarity with the Compton effect so that you would be able to navigate a passage dealing with it.

Learn the basic apparati, mechanisms and conclusions of the most significant experiments of early modern Atomic Theory including J.J. Thomson's cathode ray experiment, Millikin's oil drop experiement, and Rutherford's experiment with gold foil and alpha rays.

Be able to verbally reproduce the reasoning from evidence that led to Bohr's model of the hydrogen atom.

Master the basic description of the electronic structure of the atom in modern quantum theory in terms. Picture the orbitals of an atom. Understand how to use quantum numbers to describe them, the Pauli exclusion principle, the aufbau principle and Hund's rule.

Understand the significance of De Broglie's extension of particle-wave duality from photons to include all forms of matter and have a basic sense of the concept of wave function collapse in the context of the Heisenberg Uncertainty Principle.

Suggested Assignments

Review the basic terms for modern physics using the question server. Complete the fundamental terms crossword puzzle. Here is the solution to the puzzle.

Study the physics cards for modern physics.

Take a review tour of the modern physics web resources.

Conceptual Vocabulary for Modern Physics

Consider the relativity, cosmology, and more advanced particle physics terms optional
Basic Terms
Special relativity
Einstein's special theory of relativity not only widened the postulate of relativity but added the second postulate - that all observers will always measure the speed of light to be the same no matter what their state of uniform linear motion is.
A vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than standard atmospheric pressure.
Albert Einstein
Albert Einstein (1879 - 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and, specifically, mass-energy equivalence.
Quantum theory is the branch of physics which is based on quantization, which began in 1900 when Max Planck published his theory explaining the emission spectrum of black bodies.
Principle of relativity
A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in certain similar situations.
Speed of light
The speed of light in vacuum is the speed in a vacuum of anything having zero rest mass.
General relativity
General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915-16.
Black hole
A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon.
Time dilation
Time dilation is the phenomenon whereby an observer finds that another's clock which is physically identical to their own is ticking at a slower rate as measured by their own clock.
Length contraction
Length contraction, according to the special theory of relativity, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer.
Planck constant
The Planck constant is a physical constant that is used to describe the sizes of quanta, which plays a central role in the theory of quantum mechanics.
Photoelectric effect
The photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation.
Corresponding to most kinds of particles is an associated antiparticle with the same mass and opposite charges.
The quark is one of the two basic constituents of matter in particle physics (the other is the lepton).
Mass-energy equivalence
Mass-energy equivalence is the concept that any mass has an associated energy and vice versa.
Event horizon
The event horizon is a general term for a boundary in spacetime, such as an area surrounding the black hole, beyond which events cannot affect an outside observer.
de Broglie hypothesis
The de Broglie hypothesis is the statement that all matter (any object) has a wave-like nature, in other words, wave-particle duality.
Uncertainty principle
The Heisenberg uncertainty principle gives a lower bound on the product of the standard deviations of position and momentum for a system, implying that it is impossible for a particle to have an arbitrarily well-defined position and momentum simultaneously.
Standard Model
The Standard Model of particle physics is a quantum field theory developed between 1970 and 1973 which describes three of the four known fundamental interactions between the elementary particles that make up all matter.
The positron is the antiparticle of the electron.
Lorentz transformation
The Lorentz transformation converts between two different observers' measurements of space and time in a manner consistent with special relativity, where one observer is in constant motion with respect to the other.
Relativity of simultaneity
The relativity of simultaneity is the concept that simultaneity is not absolute, but dependent on the observer.
Compton scattering
Compton scattering is the decrease in energy of an X-ray or gamma ray photon, when it interacts with matter.
Luminiferous ether
In the late 19th century, luminiferous ether, meaning light-bearing ether, was the term used to describe a medium for the propagation of light. Today this theory is regarded as a superseded scientific theory.
Planck's law
Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a certain temperature.
Electron diffraction
Electron diffraction is a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern.
Schrödinger equation
Of central importance in non-relativistic quantum mechanics, the Schrödinger equation describes the space and time dependence of quantum mechanical systems.
Elementary particle
An elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles.
Weak interaction
The weak interaction is one of the four fundamental interactions of nature. It is due to the exchange of the heavy W and Z bosons. Its most familiar effect is beta decay.
Michelson-Morley experiment
The Michelson-Morley experiment, performed in 1887, is generally considered to be the first strong evidence against the theory of a luminiferous ether.
Lorentz factor
The Lorentz factor appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula, generally represented with a shorthand symbol.
Proper length
Proper length is an invariant quantity which is the rod distance between spacelike events in a frame of reference in which the events are simultaneous.
Proper time
Proper time is time measured by a single clock between events that occur at the same place as the clock.
Minkowski space
Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold.
World line
The world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.
Invariant mass
The invariant or intrinsic mass is a measurement or calculation of the mass of an object that is the same for all frames of reference.
Relativistic Doppler effect
The relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer, when taking into account effects of the special theory of relativity.
Work function
The work function is the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface.
Light cone
A light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime.
Minkowski diagram
A Minkowski diagram provides an illustration of the properties of space and time in the special theory of relativity, allowing a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.
Transverse Doppler effect
In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse observation.
Hermann Minkowski
Hermann Minkowski (1864 - 1909) was a Lithuanian-born German mathematician, of Jewish descent, who created and developed geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity.
Einstein field equations
The Einstein field equations are a set of ten equations in the theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy.
Vacuum energy
Vacuum energy is an underlying background energy that exists in space even when devoid of matter.
Geodesics generalize the notion of straight lines to curved spacetime in general relativity.
Gravitational time dilation
Gravitational time dilation is a consequence of Albert Einstein's theories of relativity and related theories which causes time to pass at different rates in regions of a different gravitational potential.
Gravitational redshift
Gravitational redshift describes how light of a certain wavelength originating from a source placed in a region of stronger gravitational field are found to be of longer wavelength when received by an observer in a region of weaker gravitational field.
Gravitational lens
A gravitational lens is formed when the light from a very distant, bright source is bent around a massive object, such as a galaxy, between the source object and the observer.
Gravitational singularity
A gravitational singularity is, approximately, a place where quantities which are used to measure the gravitational field become infinite.
Quantization is a procedure for constructing a quantum field theory starting from a classical field theory.
Fermi energy
The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature.
Ultraviolet catastrophe
The ultraviolet or the Rayleigh-Jeans catastrophe was a false prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power.
Compton wavelength
The Compton wavelength can be thought of as a fundamental limitation on measuring the position of a particle, taking quantum mechanics and special relativity into account.
Quantum decoherence
Quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior and give the appearance of wavefunction collapse
Schrödinger's cat
Schrödinger's cat is a seemingly paradoxical thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of the Copenhagen interpretation when going from subatomic to macroscopic systems.
Quantum entanglement
Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated.
Probability amplitude
A probability amplitude is a complex-valued function that describes an uncertain or unknown quantity such as the position of a particle in the form of a wave function, expressed as a function of position.
Wave packet
A wave packet is an envelope containing an arbitrary number of wave forms. In quantum mechanics this is interpreted to be a probability wave describing the probability that a particle or particles in a particular state will be measured to have a given position or momentum.
Quantum chromodynamics
Quantum chromodynamics is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in hadrons such as the proton, neutron or pion.
Color confinement
Color confinement is the physics phenomenon that color charged particles such as quarks cannot be isolated but are confined with other quarks by the strong interaction to form pairs or triplets so that the net color is neutral.
Fermions are particles with half-integer spin, such as protons and electrons.
Flavor is a quantum number of elementary particles related to their weak interactions.
A lepton is a fermion that does not experience the strong interaction such as the electron, the muon, and the tau, distinct from the other known family of fermions, the quarks.
Bremsstrahlung is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus.
Distinguished from fermions, which are matter particles, by their integer spin, bosons are force carrier particles such as the photon, for example.
Strong interaction
The strong interaction is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves.
Advanced terms that may appear in context in MCAT passages
Poincaré group
The Poincaré group is the group of isometries of Minkowski spacetime.
Causal spacetime structure
Causal spacetime structure refers to the description of spacetime using curves that describe the temporal relation between events.
Lorentz covariant
A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group.
Vacuum solution
A vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically, so that no matter or non-gravitational fields are present.
Schwarzschild metric
The Schwarzschild in Einstein's theory of general relativity describes the gravitational field outside a spherical, non-rotating mass such as a non-rotating star, planet, or black hole.
Schwarzschild radius
The Schwarzschild radius is a characteristic radius associated with every mass where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a gravitational singularity.
Closed timelike curve
A closed timelike curve is a worldline of a material particle in spacetime that returns to its starting point. If CTCs exist, their existence would seem to imply at least the theoretical possibility of making a time machine.
Hawking radiation
Hawking radiation is a thermal radiation predicted to be emitted by black holes due to quantum effects.
Micro black hole
A micro black hole, also called a quantum mechanical black hole and inevitably a mini black hole, is simply a tiny black hole for which quantum mechanical effects play an important role.
Quantum gravity
Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics with general relativity.
Supermassive black hole
A supermassive black hole is a black hole with a mass of an order of magnitude between hundreds of thousands and tens of billions of solar masses.
Gravitational collapse
Gravitational collapse in astronomy is the inward fall of a massive body under the influence of the force of gravity.
Einstein ring
A Chwolson ring or Einstein ring is the deformation of the light from a source such as a galaxy or star into a ring through gravitational deflection of the source's light by a lens such as another galaxy, or a black hole.
Photon gas
The photon gas is a framework for treating electromagnetic radiation as having many of the same properties of a conventional gas like hydrogen or neon - including pressure, temperature, and entropy.
A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid.
Quantum field theory
Quantum field theory provides a theoretical framework in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed.
Davisson-Germer experiment
In the Davisson-Germer experiment, which provided a critically important confirmation of the de Broglie hypothesis, the angular dependence of reflected electron intensity was measured, and was determined to have a predictable diffraction pattern.
Correspondence principle
The correspondence principle of Bohr and Heisenberg states that the quantum mechanical description of large systems should closely approximate to the classical description.
Copenhagen interpretation
The Copenhagen interpretation is a very influential interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating around 1927.
Many-worlds interpretation
Viewing history as a many-branched tree where every possible branch is realized, the many-worlds interpretation of quantum mechanics explains the appearance of wavefunction collapse with the mechanism of quantum decoherence.
Perturbation theory
Perturbation theory is a set of approximation schemes for describing a complicated quantum system in terms of a simpler one, starting with a simple system and gradually turning on an additional perturbing Hamiltonian representing a weak disturbance to the system.
Asymptotic freedom
Asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances.
Up quark
The up quark is a particle described by the Standard Model theory of physics. It is a first-generation quark with a charge of +(2/3)e. It is the lightest of all quarks.
Down quark
The down quark is a first-generation quark with a charge of -(1/3)e. It is the second-lightest of all quarks. This particle and the up quark are the fundamental constituents of the nucleons
Charm quark
The charm quark is a second-generation quark with a charge of +(2/3)e. It is the third most massive of the quarks, at 1.3 GeV (a bit more than the mass of the proton).
Strange quark
The strange quark is a second-generation quark with a charge of -(1/3)e. It is the third lightest quark after the up and down quarks, with a mass of somewhere between 80 and 130 MeV.
Top quark
The top quark is the third-generation up-type quark with a charge of +(2/3)e. It is by far the most massive of known elementary particles. Its mass is nearly as great as a gold nucleus.
Bottom quark
The bottom quark is a third-generation quark with a charge of -(1/3)e. This quark possesses a distinctive signature that makes it relatively easy to identify experimentally
Gauge boson
Gauge bosons are bosonic particles which act as carriers of the fundamental forces of nature.
Gauge theory
Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally.
W and Z bosons
The W and Z bosons are the elementary particles that mediate the weak force.
String theory
String theory is a model of fundamental physics, whose building blocks are one-dimensional extended entities rather than the zero-dimensional point particles that form the basis for the standard model of particle physics.
Gluons are elementary particles that cause quarks to interact, and are indirectly responsible for the binding of protons and neutrons together in atomic nuclei.
The baryons are the family of subatomic particles which are made of three quarks. The family notably includes the proton and neutron, which make up the atomic nucleus.
Fermionic condensate
A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures.
Trouton-Rankine experiment
The Trouton-Rankine experiment was an experiment designed to measure if the Lorentz-FitzGerald contraction of an object according to one frame produced a measurable effect in the rest frame of the object.
Einstein tensor
The Einstein tensor is a mathematical entity expressing the curvature of spacetime in the Einstein field equations, thus describing gravitation according to the theory of general relativity.
Riemannian manifold
A Riemannian manifold is a real differentiable manifold in which each tangent space is equipped with an inner product in a manner which varies smoothly from point to point.
Hilbert space
The concept of a Hilbert space generalizes the notion of Euclidean space extending methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces.
Einstein-Hilbert action
The Einstein-Hilbert action is a mathematical object that is used to derive Einstein's field equations of general relativity.
Einstein-Cartan theory
Einstein-Cartan theory in theoretical physics extends general relativity to the problem of spin angular momentum.
Gibbons-Hawking-York boundary term
The Gibbons-Hawking-York boundary term is a term that needs to be added to the Einstein-Hilbert action when the underlying spacetime manifold has a boundary.
Reissner-Nordström metric
The Reissner-Nordström metric is a solution to the Einstein field equations in empty space, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body.
Kerr metric
The Kerr metric describes the geometry of spacetime around a rotating massive body in general relativity.
Cauchy horizon
A Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem. One side contains closed space-like geodesics and the other side contains closed time-like geodesics.
Stress-energy tensor
The stress-energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime.
Stellar black hole
A stellar black hole is a black hole formed by the gravitational collapse of a star of three or more solar masses at the end of its lifetime. The process is observed as a supernova explosion or as a gamma ray burst.
No-hair theorem
The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations can be completely characterized by three externally observable classical parameters: mass, electric charge, and angular momentum.
Photon sphere
A photon sphere is a spherical region of space where gravity is strong enough that photons of light are forced to travel in orbits.
Naked singularity
In general relativity, a naked singularity is a theoretically postulated gravitational singularity without an event horizon.
Geodetic effect
The geodetic effect represents the effect of the curvature of spacetime on a spinning, moving body.
Frame-dragging is the term for the prediction of general relativity that rotating bodies drag spacetime around themselves.
Klein-Nishina formula
The Klein-Nishina formula provides an accurate prediction of the angular distribution of x-rays and gamma-rays incident upon a single electron.
Neutron interferometer
A neutron interferometer is a device capable of diffracting neutrons.
Ehrenfest theorem
The Ehrenfest theorem relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system.
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation providing a description of elementary half-spin particles, such as electrons, consistent with both quantum mechanics and special relativity.
Quantum Monte Carlo
Quantum Monte Carlo is a large class of computer algorithms that simulate quantum systems with the idea of solving the many-body problem.
Density functional theory
Density functional theory is a quantum mechanical theory used in physics and chemistry to investigate the ground state of many-body systems, in particular atoms, molecules and the condensed phases.
WKB approximation
The WKB approximation is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing.
Spontaneous parametric down conversion
Spontaneous parametric down-conversion is an important process in quantum optics in which a nonlinear crystal splits incoming photons into pairs of photons of lower energy whose combined energy and momentum are equal to the energy and momentum of the original photon.
Pauli equation
The Pauli equation is a Schrödinger equation which describes the time evolution of spin 1/2 particles. It is the non-relativistic border case of the Dirac equation and can be used where particles are slow enough that relativistic effects can be neglected.
CP violation is a violation of the postulated symmetry of the laws of physics which plays an important role in theories of cosmology that attempt to explain the dominance of matter over antimatter in the present Universe.
Cabibbo-Kobayashi-Maskawa matrix
In the standard model of particle physics the Cabibbo-Kobayashi-Maskawa matrix is a unitary matrix which contains information on the strength of flavour-changing weak decays.
QCD matter
Quark or QCD matter refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons, postulated to occur at extremely high temperatures and densities.
A strangelet or strange nugget is a hypothetical object, consisting of a bound state of roughly equal numbers of up, down, and strange quarks.
Quarkonium designates a flavorless meson whose constituents are a quark and its own antiquark.
The muon is an elementary particle with negative electric charge and a spin of 1/2. It's a mean lifetime of 2.2 microseconds is longer than any other unstable lepton, meson or baryon except for the neutron.
A glueball is a strongly-interacting particle containing no valence quarks. It is composed entirely of gluons. Such a state is possible because gluons carry color charge and experience the strong interaction.
Higgs boson
The Higgs boson, also known as the God particle, is a hypothetical massive scalar elementary particle predicted to exist by the Standard Model of particle physics.
The graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory.
A hadron is any strongly interacting composite subatomic particle such as a baryon (proton or neutron) or meson.
A meson is a strongly interacting boson, in other words, a hadron with integral spin.
A hyperon is any subatomic particle which is a baryon with non-zero strangeness, but with zero charm and zero bottomness.
Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force.
A kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. In the quark model they are understood to contain a single strange quark (or antiquark).
Deconfinement refers to a phase of matter in which quarks and gluons are free to move over distances larger than a femtometer.
Gluon condensate
The gluon condensate is a non-perturbative property of the QCD vacuum which could be partly responsible for giving masses to certain hadrons.