Physical Chemistry 2 Exam 1 UTC – Flashcards

Unlock all answers in this set

Unlock answers
question
blackbody
answer
A blackbody is an idealized object that emits and absorbs all frequencies. A true blackbody does not exist, but a close approximation can be made for labs.
question
blackbody radiation
answer
Blackbody radiation is the emission of radiation from a black body. Its study led to the development of quantum mechanics due to classical physics' failure to explain it properly. It was improperly described by the Raleigh Jeans law, properly described by Max Planck.
question
Wien displacement law (give f)
answer
The Wein displacement law is the relationship between the wavelength at the maximum intensity and the temperature. They are indirectly proportional.
question
ultraviolet catastrophe
answer
Ultraviolet catastrophe represents the classical interpretation of the blackbody radiation that predicted emitted radiation of large intensities in the UV region; property that is not experimentally observed.
question
Planck constant
answer
The Planck constant is h. It is the constant that relates frequency to energy in E=hnu and pops up all over quantum mechanics. The units imply action. Discovered by Max Planck.
question
photoelectrons
answer
are electrons emitted during the photoelectric effect due to a photon of light hitting a surface with the required threshold frequency.
question
photon
answer
a photon is a small packet (quanta) of energy the form of electromagnetic radiation.
question
threshold frequency
answer
The property of metallic surfaces to emit electron upon irradiation is called the photoelectric effect. The threshold frequency (0) is a limit of the radiation frequency below which the photoelectric effect is not observed. The threshold frequency is related to the work function by: = hnu_o
question
work function
answer
The property of metallic surfaces to emit electron upon irradiation is called the photoelectric effect. The minimum energy required to remove an electron from the surface of a particular metal is the work function
question
line spectra
answer
is the emission spectra of an atom showing isolated lines at specific discrete frequencies and can be used as a fingerprint for the element.
question
Lyman, Balmer, Pashen, Bracket series
answer
The Lyman series is UV. goes to n =1 The Balmer series is a series of lines in the spectrum of H atom, corresponding to transitions from n = 3,4,5,... to n = 2. This series of lines appear mostly in the visible range of radiation. The Pashen series is mostly in the near infrared region. goes to n = 3 The Bracket series is the infrared region. goes to n=4.
question
series limit
answer
The series limit is the frequency that is converged on by line spectra in a seires. It is the result of the energy being emitted by returning to a lower energy level (n1) from a higher energy level (n2). The limit is reached as n2 approaches infinity.
question
Balmer formula
answer
describes the balmer series, the emission spectrum of hyrogen in visible region
question
Rydberg formula
answer
A general equation for the emission line spectra of hydrogen. It uses the rydberg constant, orginally found experimentally, looks at transitions from higher energy states to lower energy states.
question
Rydberg constant
answer
The rydberg constant is originally determined experimentally by Rydberg, but was later derived from serveral other constants in the Bohr Model.
question
angular momentum
answer
the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity.
question
stationary state or orbit
answer
is the location and path of the bohr model of hydrogen at discrite positions. It is required so that the electron does not accelarate into the nucleus due to Columbic charges.
question
first Bohr radius
answer
is the smallest allowed radius of an electron's orbit in the Bohr model.
question
ground state
answer
is the lowest level the electron can occupy. In a system for the bohr model it is n=1, while for the harmonic oscillator it is n=0. States other than the ground state are called excited states.
question
excited states
answer
Excited states are states of higher energy than the ground state.
question
Bohr frequency condition
answer
is that the frequency of the electron during a transition from one electron state to another is related to the change in energy. DeltaE=hnu
question
wave-particle duality
answer
is the phenomena that light and all of matter acts both like a wave and like a particle to a certain degree, depending on mass, velocity, and plancks constant
question
de Broglie wavelength
answer
The movement of any particle has some wavelike character, and the de Broglie wavelength is the wavelength associated with the moving particle. This wavelength is given by
question
Heisenberg Uncertainty Principle
answer
Two properties for which the operators do not commute (like the position and the momentum or the energy and time) cannot be known (or measured) simultaneously with any arbitrary precision.
question
Schrödinger equation
answer
The schrodinger equation is the equation for finding the wavefunction of a particle, and is based on the idea of wave-particle duality. It can be written as time-independent or time-dependent, and its solutions are called stationary state wavefunctions. It can be simplified to GIVE using operators.
question
wavefunctions
answer
A wavefunction psi is a solution of the Schrödinger equation for a particular system. The most important property of the wavefunction if that psi*psi dx gives the probability of finding the particle at a certain position.
question
operator
answer
an operator is a symbol that tells you to do something to whatever follows the symbol.
question
operand
answer
is the quantity that an operation is performed on, as dictated by the operator.
question
Laplacian operator
answer
A operator that signifies that the second partial derivative should be taken to x, y, and z.
question
Hamiltonian operator
answer
The Hamiltonian operator is the operator for total energy, and is the sum of the operator for kinetic energy and the operator for the potential energy: The Hamiltonian eigenvalue is the total energy. A node is a geometric location (point, line, surface, etc.) where the wavefunction (or the amplitude of the wave) is zero.
question
eigenvalue-eigenfunction relation
answer
An eigenfunction is a function that is retained after an operation is performed on it, dictated by the operator. The eigenvalue is a constant that is multiplied against the eigenfunction after the operation. A^*phi=alpha*phi
question
complex conjugate
answer
the complex conjugate of the wavefunction is obtained by replacing i with -i in the expression of the wavefunction. Multiplying psi*psi gives a real product.
question
Hermitian operator
answer
a hermitian operator is a linear operator that exists in quantum mechanics for every observable in classic physics An operator is hermitian if it is linear and if the integral over psi1*A^psi2 = integral over psi2(A^psi1)
question
observable
answer
is a measurable dynamic value such as energy, position, momentum, etc
question
normalized/normalizable
answer
A wavefunction being normalized is a condition that must be satisfied to properly represent the probability of finding the particle. It means that the integral over the wavefunction times its complex conjugate must be one. Normalizable - ?
question
commutation
answer
Is a property of operators in which A^B^f(x) = B^A^f(x). Operators generally do not commute.
question
commutator
answer
is [A^,B^] = A^B^-B^A^ The commutator of commuting operators is the zero operator.
question
linear operators
answer
an operator is linear if it is distributive over two functions and their constants
question
variance/standard deviation
answer
The varience is the square of the standard deviaton The standard deviation is a representation of the uncertainty in a measurement, whether two uncertainties they can both be determined with arbitrary precision is related to their product and the commutator.
question
orthogonal
answer
If integral of (psi^*_i)(psi_j) is zero
question
orthonormal
answer
If integral of (psi^*_i)(psi_j) is one and i = j
question
even function
answer
An even function is a function for which f(x) = f(-x). An even function is always orthogonal to an odd function over an interval centered at 0.
question
odd function
answer
? An odd function is a function for which f(x) = -f(-x). An even function is always orthogonal to an odd function over an interval centered at 0.
question
complete set
answer
complete set of commuting observables (CSCO) is a set of commuting operators whose eigenvalues completely specify the state of a system.[1] 'set from which all elements of our space can be constructed by linear combination
question
particle-in-a-box
answer
The particle-in-a-box refers to the quantum mechanical treatment of translational motion. b. One tries to solve the Schrödinger equationto obtain the wavefunctions and the allowed energies for the particle
question
normalization constant
answer
allows the function to be normalized
question
probability density
answer
probability that particle is located in that region orbital uses, what is typically represented is the boundary surface of the orbital, which is the surface (of equal electron density) that contains 90% of electron density.
question
free-electron model
answer
model of valence electrons in a crystalline metallic solid
question
Correspondence Principle
answer
Quantum mechanics results and classical mechanics results tend to agree in the limit of large quantum numbers. The large-quantum-number limit is called the classical limit.
question
classical limit
answer
This is an illustration of the Correspondence Principle that says that quantum mechanics results and classical mechanics results tend to agree in the limit of large quantum numbers. ? The large-quantum-number limit is called the classical limit.
question
separable Hamiltonian
answer
separating the hamiltonian into different dimensions
question
harmonic oscillator
answer
The harmonic oscillator refers to the quantum mechanical treatment of vibrational motion The quantum-mechanical harmonic oscillator model accounts for the IR spectrum of a diatomic molecule.
question
reduced mass
answer
The movement of a two-body system can be replaced by the movement of a one-body system where the mass is replaced with the reduced mass
question
Hermite polynomials
answer
polynomial functions used in harmonic oscillator wavefunctions
question
zero-point energy
answer
Is the residual energy of the harmonic oscillator, it is different (i.e., bigger) than zero, and it is obtained for vibrational quantum number n = 0
question
selection rule
answer
The transitions between various levels in harmonic oscillator model follow the selection rule:
question
fundamental vibrational frequency
answer
The quantum-mechanical harmonic oscillator predicts the existence of only one frequency in the spectrum of a diatomic, the frequency called fundamental vibrational frequecy
question
tunneling
answer
The quantum mechanical particles have the property of non-zero probability in regions forbidden by classical mechanics.
question
rigid rotator
answer
The rigid rotator (or rigid rotor) refers to the quantum mechanical treatment of rotational motion. b. The quantum mechanical rigid rotator is a model for a rotating diatomic molecule.
question
moment of inertia
answer
analague to mass in rotational motion
question
spherical harmonic functions
answer
angular portion of wavefunction, rigid rotor wavefunctions
question
degeneracy
answer
Degeneracy represents the property of two or more eigenfunctions (or wavefunctions) having the same eigenvalue. The energy is one possible such eigenvalue.
question
microwave spectroscopy
answer
transitions between energy states of rotational motion, rigid rotor model
question
rotational constant
answer
write the frequency in terms of the rotational constant B
question
spherical coordinates
answer
r, phi, theta
question
angular momentum
answer
analogue to linear momentum, inertia times angular velocity
question
atomic orbitals
answer
term used to represent the wavefunctions are that depend on 3 quantum numbers, the boundary surface, or the probability density
question
Legendre polynomials
answer
the P stuff in HAM model angular wavefunctions
question
angular momentum magnitude
answer
L=hbar sqrt(L(L+1)
question
associated Laguerre polynomials
answer
polynomials for radial hydrogen wavefunctions
question
boundary surface
answer
the boundary surface of the orbital, which is the surface (of equal electron density) that contains 90% of electron density.
question
most probable value of r
answer
most probable radius of 1s orbital is the first bohr radius
question
principal quantum number
answer
The principal quantum number n: a. Can take values of n = 1,2,... b. It describes the shell or level.
question
azimuthal/secondary/orbital quantum number
answer
The angular momentum quantum number l: a. It is also called azimuthal or secondary or orbital quantum number. b. Can take values between 0 and n-1: l = 0,1,...,n-1 c. It describes the type of subshell (or shape of orbital), and, in addition to n, the actual subshell or sublevel. determined angular momentum
question
magnetic quantum number
answer
he magnetic quantum number m: a. More specifically denoted m l as we will see later. b. It can take (2l + 1) values: l m ,..., 2 , 1 , 0 ? Same as the degeneracy of the l sublevel or subshell. c. It describes the orientation (or type) of orbitals, and, in addition to n and l, the actual orbital. d. Quantum number m completely determine the z component of the angular momentum (L z ): m L z e. The quantum number m is called magnetic because the energy of hydrogen atom in a magnetic field depends on m.
question
Separation of Variables
answer
It is a technique of solving multivariable equations. In particular, solving Schrodinger equation by writing the Hamiltonian as a sum of terms leads to the overall wavefunction to be the product of functions
question
Zeeman effect
answer
Each energy level has a degeneracy of (2l + 1) which is removed in magnetic field. ? This is knows as the Zeeman e
Get an explanation on any task
Get unstuck with the help of our AI assistant in seconds
New