Key Terms and Index
Key Terms
Key Terms: Chapter 1
- classical (Galilean) velocity addition
- method of adding velocities when v<<c; velocities add like regular numbers in one-dimensional motion: u=v+u′, where v is the velocity between two observers, u is the velocity of an object relative to one observer, and u′ is the velocity relative to the other observer
- event
- occurrence in space and time specified by its position and time coordinates (x, y, z, t) measured relative to a frame of reference
- first postulate of special relativity
- laws of physics are the same in all inertial frames of reference
- Galilean relativity
- if an observer measures a velocity in one frame of reference, and that frame of reference is moving with a velocity past a second reference frame, an observer in the second frame measures the original velocity as the vector sum of these velocities
- Galilean transformation
- relation between position and time coordinates of the same events as seen in different reference frames, according to classical mechanics
- inertial frame of reference
- reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force
- length contraction
- decrease in observed length of an object from its proper length L0 to length L when its length is observed in a reference frame where it is traveling at speed v
- Lorentz transformation
- relation between position and time coordinates of the same events as seen in different reference frames, according to the special theory of relativity
- Michelson-Morley experiment
- investigation performed in 1887 that showed that the speed of light in a vacuum is the same in all frames of reference from which it is viewed
- proper length
- L0; the distance between two points measured by an observer who is at rest relative to both of the points; for example, earthbound observers measure proper length when measuring the distance between two points that are stationary relative to Earth
- proper time
- Δτ is the time interval measured by an observer who sees the beginning and end of the process that the time interval measures occur at the same location
- relativistic kinetic energy
- kinetic energy of an object moving at relativistic speeds
- relativistic momentum
- p→, the momentum of an object moving at relativistic velocity; p→=γmu→
- relativistic velocity addition
- method of adding velocities of an object moving at a relativistic speeds
- rest energy
- energy stored in an object at rest: E0=mc2
- rest frame
- frame of reference in which the observer is at rest
- rest mass
- mass of an object as measured by an observer at rest relative to the object
- second postulate of special relativity
- light travels in a vacuum with the same speed c in any direction in all inertial frames
- special theory of relativity
- theory that Albert Einstein proposed in 1905 that assumes all the laws of physics have the same form in every inertial frame of reference, and that the speed of light is the same within all inertial frames
- speed of light
- ultimate speed limit for any particle having mass
- time dilation
- lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location)
- total energy
- sum of all energies for a particle, including rest energy and kinetic energy, given for a particle of mass m and speed u by E=γmc2, where γ=11−u2c2
- world line
- path through space-time
Key Terms: Chapter 2
- absorber
- any object that absorbs radiation
- absorption spectrum
- wavelengths of absorbed radiation by atoms and molecules
- Balmer formula
- describes the emission spectrum of a hydrogen atom in the visible-light range
- Balmer series
- spectral lines corresponding to electron transitions to/from the n=2 state of the hydrogen atom, described by the Balmer formula
- blackbody
- perfect absorber/emitter
- blackbody radiation
- radiation emitted by a blackbody
- Bohr radius of hydrogen
- radius of the first Bohr’s orbit
- Bohr’s model of the hydrogen atom
- first quantum model to explain emission spectra of hydrogen
- Brackett series
- spectral lines corresponding to electron transitions to/from the n=4 state
- Compton effect
- the change in wavelength when an X-ray is scattered by its interaction with some materials
- Compton shift
- difference between the wavelengths of the incident X-ray and the scattered X-ray
- Compton wavelength
- physical constant with the value λc=2.43pm
- cut-off frequency
- frequency of incident light below which the photoelectric effect does not occur
- cut-off wavelength
- wavelength of incident light that corresponds to cut-off frequency
- Davisson–Germer experiment
- historically first electron-diffraction experiment that revealed electron waves
- de Broglie wave
- matter wave associated with any object that has mass and momentum
- de Broglie’s hypothesis of matter waves
- particles of matter can behave like waves
- double-slit interference experiment
- Young’s double-slit experiment, which shows the interference of waves
- electron microscopy
- microscopy that uses electron waves to “see” fine details of nano-size objects
- emission spectrum
- wavelengths of emitted radiation by atoms and molecules
- emitter
- any object that emits radiation
- energy of a photon
- quantum of radiant energy, depends only on a photon’s frequency
- energy spectrum of hydrogen
- set of allowed discrete energies of an electron in a hydrogen atom
- excited energy states of the H atom
- energy state other than the ground state
- Fraunhofer lines
- dark absorption lines in the continuum solar emission spectrum
- ground state energy of the hydrogen atom
- energy of an electron in the first Bohr orbit of the hydrogen atom
- group velocity
- velocity of a wave, energy travels with the group velocity
- Heisenberg uncertainty principle
- sets the limits on precision in simultaneous measurements of momentum and position of a particle
- Humphreys series
- spectral lines corresponding to electron transitions to/from the n=6 state
- hydrogen-like atom
- ionized atom with one electron remaining and nucleus with charge +Ze
- inelastic scattering
- scattering effect where kinetic energy is not conserved but the total energy is conserved
- ionization energy
- energy needed to remove an electron from an atom
- ionization limit of the hydrogen atom
- ionization energy needed to remove an electron from the first Bohr orbit
- Lyman series
- spectral lines corresponding to electron transitions to/from the ground state
- nuclear model of the atom
- heavy positively charged nucleus at the center is surrounded by electrons, proposed by Rutherford
- Paschen series
- spectral lines corresponding to electron transitions to/from the n=3 state
- Pfund series
- spectral lines corresponding to electron transitions to/from the n=5 state
- photocurrent
- in a circuit, current that flows when a photoelectrode is illuminated
- photoelectric effect
- emission of electrons from a metal surface exposed to electromagnetic radiation of the proper frequency
- photoelectrode
- in a circuit, an electrode that emits photoelectrons
- photoelectron
- electron emitted from a metal surface in the presence of incident radiation
- photon
- particle of light
- Planck’s hypothesis of energy quanta
- energy exchanges between the radiation and the walls take place only in the form of discrete energy quanta
- postulates of Bohr’s model
- three assumptions that set a frame for Bohr’s model
- power intensity
- energy that passes through a unit surface per unit time
- propagation vector
- vector with magnitude 2π/λ that has the direction of the photon’s linear momentum
- quantized energies
- discrete energies; not continuous
- quantum number
- index that enumerates energy levels
- quantum phenomenon
- in interaction with matter, photon transfers either all its energy or nothing
- quantum state of a Planck’s oscillator
- any mode of vibration of Planck’s oscillator, enumerated by quantum number
- reduced Planck’s constant
- Planck’s constant divided by 2π
- Rutherford’s gold foil experiment
- first experiment to demonstrate the existence of the atomic nucleus
- Rydberg constant for hydrogen
- physical constant in the Balmer formula
- Rydberg formula
- experimentally found positions of spectral lines of hydrogen atom
- scattering angle
- angle between the direction of the scattered beam and the direction of the incident beam
- Stefan–Boltzmann constant
- physical constant in Stefan’s law
- stopping potential
- in a circuit, potential difference that stops photocurrent
- wave number
- magnitude of the propagation vector
- wave quantum mechanics
- theory that explains the physics of atoms and subatomic particles
- wave-particle duality
- particles can behave as waves and radiation can behave as particles
- work function
- energy needed to detach photoelectron from the metal surface
- α-particle
- doubly ionized helium atom
- α-ray
- beam of α-particles (alpha-particles)
- β-ray
- beam of electrons
- γ-ray
- beam of highly energetic photons
Key Terms: Chapter 3
- anti-symmetric function
- odd function
- Born interpretation
- states that the square of a wave function is the probability density
- complex function
- function containing both real and imaginary parts
- Copenhagen interpretation
- states that when an observer is not looking or when a measurement is not being made, the particle has many values of measurable quantities, such as position
- correspondence principle
- in the limit of large energies, the predictions of quantum mechanics agree with the predictions of classical mechanics
- energy levels
- states of definite energy, often represented by horizontal lines in an energy “ladder” diagram
- energy quantum number
- index that labels the allowed energy states
- energy-time uncertainty principle
- energy-time relation for uncertainties in the simultaneous measurements of the energy of a quantum state and of its lifetime
- even function
- in one dimension, a function symmetric with the origin of the coordinate system
- expectation value
- average value of the physical quantity assuming a large number of particles with the same wave function
- field emission
- electron emission from conductor surfaces when a strong external electric field is applied in normal direction to conductor’s surface
- ground state energy
- lowest energy state in the energy spectrum
- Heisenberg’s uncertainty principle
- places limits on what can be known from a simultaneous measurements of position and momentum; states that if the uncertainty on position is small then the uncertainty on momentum is large, and vice versa
- infinite square well
- potential function that is zero in a fixed range and infinitely beyond this range
- momentum operator
- operator that corresponds to the momentum of a particle
- nanotechnology
- technology that is based on manipulation of nanostructures such as molecules or individual atoms to produce nano-devices such as integrated circuits
- normalization condition
- requires that the probability density integrated over the entire physical space results in the number one
- odd function
- in one dimension, a function antisymmetric with the origin of the coordinate system
- position operator
- operator that corresponds to the position of a particle
- potential barrier
- potential function that rises and falls with increasing values of position
- principal quantum number
- energy quantum number
- probability density
- square of the particle’s wave function
- quantum dot
- small region of a semiconductor nanocrystal embedded in another semiconductor nanocrystal, acting as a potential well for electrons
- quantum tunneling
- phenomenon where particles penetrate through a potential energy barrier with a height greater than the total energy of the particles
- resonant tunneling
- tunneling of electrons through a finite-height potential well that occurs only when electron energies match an energy level in the well, occurs in quantum dots
- resonant-tunneling diode
- quantum dot with an applied voltage bias across it
- scanning tunneling microscope (STM)
- device that utilizes quantum-tunneling phenomenon at metallic surfaces to obtain images of nanoscale structures
- Schrӧdinger’s time-dependent equation
- equation in space and time that allows us to determine wave functions of a quantum particle
- Schrӧdinger’s time-independent equation
- equation in space that allows us to determine wave functions of a quantum particle; this wave function must be multiplied by a time-modulation factor to obtain the time-dependent wave function
- standing wave state
- stationary state for which the real and imaginary parts of Ψ(x,t) oscillate up and down like a standing wave (often modeled with sine and cosine functions)
- state reduction
- hypothetical process in which an observed or detected particle “jumps into” a definite state, often described in terms of the collapse of the particle’s wave function
- stationary state
- state for which the probability density function, |Ψ(x,t)|2, does not vary in time
- time-modulation factor
- factor e−iωt that multiplies the time-independent wave function when the potential energy of the particle is time independent
- transmission probability
- also called tunneling probability, the probability that a particle will tunnel through a potential barrier
- tunnel diode
- electron tunneling-junction between two different semiconductors
- tunneling probability
- also called transmission probability, the probability that a particle will tunnel through a potential barrier
- wave function
- function that represents the quantum state of a particle (quantum system)
- wave function collapse
- equivalent to state reduction
- wave packet
- superposition of many plane matter waves that can be used to represent a localized particle
Key Terms: Chapter 4
- angular momentum orbital quantum number (l)
- quantum number associated with the orbital angular momentum of an electron in a hydrogen atom
- angular momentum projection quantum number (m)
- quantum number associated with the z-component of the orbital angular momentum of an electron in a hydrogen atom
- atomic orbital
- region in space that encloses a certain percentage (usually 90%) of the electron probability
- Bohr magneton
- magnetic moment of an electron, equal to 9.3×10−24J/T or 5.8×10−5eV/T
- braking radiation
- radiation produced by targeting metal with a high-energy electron beam (or radiation produced by the acceleration of any charged particle in a material)
- chemical group
- group of elements in the same column of the periodic table that possess similar chemical properties
- coherent light
- light that consists of photons of the same frequency and phase
- covalent bond
- chemical bond formed by the sharing of electrons between two atoms
- electron configuration
- representation of the state of electrons in an atom, such as 1s22s1 for lithium
- fine structure
- detailed structure of atomic spectra produced by spin-orbit coupling
- fluorescence
- radiation produced by the excitation and subsequent, gradual de-excitation of an electron in an atom
- hyperfine structure
- detailed structure of atomic spectra produced by spin-orbit coupling
- ionic bond
- chemical bond formed by the electric attraction between two oppositely charged ions
- laser
- coherent light produced by a cascade of electron de-excitations
- magnetic orbital quantum number
- another term for the angular momentum projection quantum number
- magnetogram
- pictoral representation, or map, of the magnetic activity at the Sun’s surface
- metastable state
- state in which an electron “lingers” in an excited state
- monochromatic
- light that consists of photons with the same frequency
- Moseley plot
- plot of the atomic number versus the square root of X-ray frequency
- Moseley’s law
- relationship between the atomic number and X-ray photon frequency for X-ray production
- orbital magnetic dipole moment
- measure of the strength of the magnetic field produced by the orbital angular momentum of the electron
- Pauli’s exclusion principle
- no two electrons in an atom can have the same values for all four quantum numbers (n,l,m,ms)
- population inversion
- condition in which a majority of atoms contain electrons in a metastable state
- principal quantum number (n)
- quantum number associated with the total energy of an electron in a hydrogen atom
- radial probability density function
- function use to determine the probability of a electron to be found in a spatial interval in r
- selection rules
- rules that determine whether atomic transitions are allowed or forbidden (rare)
- spin projection quantum number (ms)
- quantum number associated with the z-component of the spin angular momentum of an electron
- spin quantum number (s)
- quantum number associated with the spin angular momentum of an electron
- spin-flip transitions
- atomic transitions between states of an electron-proton system in which the magnetic moments are aligned and not aligned
- spin-orbit coupling
- interaction between the electron magnetic moment and the magnetic field produced by the orbital angular momentum of the electron
- stimulated emission
- when a photon of energy triggers an electron in a metastable state to drop in energy emitting an additional photon
- transition metal
- element that is located in the gap between the first two columns and the last six columns of the table of elements that contains electrons that fill the d subshell
- valence electron
- electron in the outer shell of an atom that participates in chemical bonding
- Zeeman effect
- splitting of energy levels by an external magnetic field