Pchem 2 exam 1 vocab (ch 1, 2, 3, 4)

kms

Classical Physics

the study of the laws of nature that describe the motion and behavior of objects under normal circumstances, without taking into account the effects of quantum mechanics or relativity. predates modern, more complete, or more widely applicable theories.

Blackbody

absorbs and emits all frequencies, called an ideal body. serves as an idealization for any radiating material

Blackbody Radiation

the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body.

Boltzmann constant

k(B). 1.380649 × 10-23 m^2 kg s^-2 K^-1

Rayleigh-Jeans law

Expression derived in classical physics for the plot of the intensity of blackbody radiation versus frequency for several temperatures.

ultraviolet catastrophe

Note that the Rayleigh- Jeans law reproduces the experimental data at low frequencies. At high frequencies, however, the Rayleigh- Jeans law predicts that the radiant energy density diverges as v^2.

the frequency increases as the radiation enters the ultraviolet region. Failure of classical physics.

Planck constant

6\.62607015 × 10^-34 m^2 kg / s

Planck distribution law for blackbody radiation

Derived to solve the issue w Rayleigh-Jeans law for blackbodies, because it doesnt diverge at large frequencies

Wien displacement law

Stefan-Boltzmann law

Stefan-Boltzmann constant

sigma. 5.6697 x 10^-8 J m^-2 K^-4 s^-1

photoelectric effect

The ejection of electrons from the surface of a metal by radiation. German physicist Heinrich Hertz discovered that ultraviolet light causes electrons to be emitted from a metallic surface. experimental observations of the photoelectric effect are in stark contrast with the classical wave theory of light. Experimentally, the kinetic energy of the ejected electrons is independent of the intensity of the incident radiation.

threshold frequency

v(0). characteristic of the metallic surface, below which no electrons are ejected, regardless of the intensity of the radiation. Above v0, the kinetic energy of the ejected electrons varies linearly with the frequency v. These observations served as an embarrassing contradiction of classical theory.

photons

Einstein proposed instead that the radiation itself existed as small packets of energy, E = hv

work function

circle crossed through symbol. of a metal, is analogous to an ionization energy of an isolated atom.

kinetic energy

Einstein derived

derivations from einstein’s kinetic energy

shows that a plot of KE versus v should be linear and that the slope of the line should be h (plancks constant)

eV conversion

molar gas constant

R, 8.314 J K^-1 mol^-1

mechanical vibrations

of atoms, are subject to quantization. Einstein assumed that the oscillations of the atoms about their equilibrium lattice positions are quantized according to the formula e = nhv or delta e = hv.

law of Dulong and Petit

law states that the specific heat of an atomic solid times the atomic mass is approximately 25 J. A more fundamental, but equivalent, version of the law says that the molar heat capacity at constant volume, C(v), is equal to 3R, where R is the molar gas constant. The classical result is seen to occur at high temperatures, but C(v) decreases and goes to zero as the temperature is lowered. These low-temperature heat capacities are quite contrary to classical theory.

line spectra

every atom, when subjected to high temperatures or an electrical discharge, emits electromagnetic radiation of characteristic frequencies. each atom has a characteristic emission spectrum that consists of only certain discrete frequencies

wave number

The standard units used in spectroscopy. cm- 1

Balmer ‘s formula

Balmer series

This series of lines, the ones occurring in the visible and near ultraviolet regions of the hydrogen atomic spectrum and predicted by Balmer's formula

series limit

aka wavelength = 364.7 nm

Lyman

Balmer

n1, n2, region of spectrum

Paschen

n1, n2, region of spectrum. The term "near infrared" denotes the part of the infrared region of the spectnun that is near to the visible region.

Brackett

n1, n2, region of spectrum.

Rydberg formula

Rydberg constant

R(H). 109,677.57 cm^-1.

Ritz combination rule

describes the relationship of the spectral lines for all atoms. it is possible to find pairs of spectral lines, which have the property that the sum of their wavenumbers is also an observed spectral line.

The kinetic energy of the revolving particle

T = KE

moment of inertia

I = mr^2

Linear momentum

p = mv. fundamental quantity in linear systems

angular momentum

fundamental quantity associated with rotating systems

The Correspondences Between the Motion of Linear Systems and Rotating Systems

ground-state energy

the state of lowest energy, n=1

excited slates

states of higher energy, n=2+. generally unstable with respect to the ground state

Bohr frequency condition

Bohr frequency condition in the form of the empirical Rydberg formula

hv = hcv with \~ above the v

reduced mass µ

can be used in the rydberg constant for m(e)

Bohr frequency condition for non-hydrogen-like atoms

hydrogen-like ion = He^+ Li^2+ Be^3+

wave-particle duality of light

light appears wavelike in some instances and particle-like in others

De Broglie wavelength

also written to = h/p

The de Broglie Wavelengths of Various Moving Objects

quantum condition

Bohr quantization condition

X-ray diffraction

When a beam of X rays is directed at a crystalline substance, the beam is scattered in a definite manner characteristic of the atomic structure of the crystalline substance. occurs because the interatomic spacings in the crystal are about the same as the wavelength of the X rays.

light and matter

have the characteristics of both waves and particles

Heisenberg’s uncertainty principle

states that if we wish to locate any particle to within a distance delta x, then we automatically introduce an uncertainty in the momentum of the particle and that the uncertainty is given by the equation

Schrodinger equation

a differential equation whose solution, psi(x), describes a particle of mass m moving in a potential field described by V (x).

amplitude

The maximum displacement of something from its equilibrium horizontal position.

classical wave equation

let u(x, t) be the displacement of the string, then u (x , t) satisfies the equation. v is the speed with which a disturbance moves along the string

partial differential equation

n equation containing an unknown function of two or more variables and its partial derivatives with respect to these variables.

independent variable

a variable (often denoted by x ) whose variation does not depend on that of another.

linear partial differential equation

If the dependent variable and all its partial derivatives occur linearly in any partial differential equation (its derivatives appear only to the first power and there are no cross terms)

boundary conditions

specify the behavior of u(x, t) at the boundaries.

separation of variables

any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation

ordinary differential equations

an equation which is defined for one or more functions of one independent variable and its derivatives.

degeneracy

wave functions

solutions to the Schrodinger equation

stationary-state wave functions

Solutions to the time-independent Schrodinger equation

particle in a box

the time-independent Schrodinger equation applied to a free particle of mass m that is restricted to lie along a one-dimensional interval of length a.

spatial amplitude

of a wave

h-bar

operator

a symbol that tells you to do something to whatever follows the symbol. i.e. dy/dx or d/dx, SQRT, integral symbol & dx, a constant in front of a value, etc. Denoted as the A in the image.

linear operators

c1 and c2 are constants. the picture shows a method that proves this

eigenfunction

in an eigenvalue equation, the function of an operator A and eigenvalue a

eigenvalue

The constant a

eigenvalue problem

Determining the function and constant of a given operator

Schrodinger equation as an eigenvalue problem

Hamiltonian operator

The wave function is an eigenfunction, and the energy is an eigenvalue of this. If V(x) = 0, the energy is all kinetic energy and can be defined as an operator T

Kinetic energy operator

momentum operator

\

problem of a particle in a one-dimensional box

the case of a free particle of mass m constrained to lie along the x axis between x = 0 and x =a

free particle

experiences no potential energy. V (x) = 0. Equation in 1-D box

probability that the particle is located between x and x + dx

quantum number

integer n, seen in this equation and many others. related to excitement state of electrode

energy of a particle

The wave function corresponding to the energy of a particle

energy levels, wave functions (a), and probability densities (b) for the particle in a box

free-electron model energy-level scheme example

for butadiene

normalized wave function

satisfied this equation

normalization. constant

the constant that multiplies a wave function is adjusted to assure that Equation 3.24 is satisfied

correspondence principle

quantum-mechanical results and classical-mechanical results tend to agree in the limit of large quantum numbers. the particle tends to behave classically in the limit of large n (fairly uniformly distributed). The large quantum number limit is often called the classical limit

root-mean-square momentum

Heisenberg uncertainty principle

three-dimensional particle in a box

the particle is confined to lie within a rectangular parallelepiped with sides of lengths a, b, and c

Schrodinger equation for a three-dimensional particle in a box

Laplacian operator

The energy levels for a particle in a cube, showing degeneracies

dynamical variables

quantities such as position, momentum, angular momentum, and energy

observable

A measurable dynamical variable

trajectory

The vector r (t) describes the position of the particle as a function of time, and is known as this property.

Postulate 1

The state of a quantum-mechanical system is completely specified by a function psi (r, t) that depends on the coordinates of the particle and on time. This function, called the wave function or state function, has the important property that psi\*(r, t)psi(r, t)dxdydz is the probability that the particle lies in the volume element dxdydz located at r at time t.

Postulate 2

To every observable in classical mechanics there corresponds a linear, Hermitian operator in quantum mechanics

Classical-Mechanical Observables and Their Corresponding Quantum-Mechanical Operators

Postulate 3

In any measurement of the observable associated with the operator A, the only values that will ever be observed are the eigenvalues a, which satisfy the eigenvalue equation