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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 
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

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