PHYSICAL CHEMISTRY - ACS
QUANTUM MECHANICS FINAL EXAM
who assumed the energy of all oscillators in a blackbody was quantized? what was it
said to be quantized by? - Correct Answers -Planck; e=nhv where n=quantum number,
h=Planks constant, and v=frequency of the oscillator
what did Einstein propose through use of Plank's quantization of energy theory? -
Correct Answers -that radiation itself existed as packets of energy (called photons) with
e=hv
what is the empirical equation explaining the observed spectrum of hydrogen? - Correct
Answers -v=Rh((1/n1^2)-(1/n2^2)) where Rh is the Rydberg constant, and n1 and n2
are quantum numbers
the angular momentum of the hydrogen atom is quantized by units of what? - Correct
Answers -h/2Pi or hbar
what is the relation of momentum to wavelength? (de Broglie relation) - Correct
Answers -wavelength=h/p or h/m*v
where v is velocity, m is mass, and h is planck's constant
what is the Schrodinger equation? - Correct Answers -a partial differential equation
describing the wave properties of matter. solutions are called wave functions.
equation for the theory that two electrons cannot occupy the same spatial orbital unless
they are of opposite spin? (Pauli exclusion principle) - Correct Answers -Ψ(1,2)= -Ψ(2,1)
what is the equation for the Heisengburg uncertainty principle? - Correct Answers -ΔxΔp
is greater than or equal to 0.5hbar
what does the correspondence principle state? - Correct Answers -classical and
quantum mechanical results merge in the limit of high quantum numbers
What is the time independent schrodinger equation? - Correct Answers -HΨ=EΨ where
H is the hamiltonian operator and E is the energy
, when is a function an eigen function? - Correct Answers -example: A is an eigen
function if applying A to the function f is the same as the multiplication of f by a constant,
a. Or Af=af
the wavefunctions and energies of systems are _____ of the Hamiltonian operator -
Correct Answers -eigen functions. In other words, applying the Hamiltonian to the wave
function is the same as multiplying the wavefunction by the constant, E or energy.
what is an operator? - Correct Answers -A rule for changing one function into another
function
what makes an operator linear? - Correct Answers -it (represented by A) satisfies the
equation: A(cf+dg)=Acf+Adg where f and g are functions and c and d are constants
what makes an operator Hermitian? - Correct Answers -it (represented by A) satisfies
the equation: INTEGRAL(fAg dT) = INTEGRAL(gAf dT)
what is the Born-Oppenheimer approximation? - Correct Answers -because the
electrons in molecules move much more quickly than the nucleus, we assume the
nucleus is fixed
what is the Fanck-Condon principle? - Correct Answers -because nuclei are much more
massive than electrons, en electronic transition takes place in the presence of a fixed
nucleus
why isn't every solution to the Schrondinger equation acceptable? - Correct Answers -
because of boundary conditions for each given problem. Also, the wave function must
be continuous, continually differentiablex, single-valued (i.e. can't have 2 possible Y
values for one X value), finite-valued (i.e. can't go to infinity), and able to be normalized
over the appropriate range
when a set is orthogonal what happens? - Correct Answers -INTEGRAL(Ψ*Ψ dT)=0
wave functions that are solutions to a given Hamiltonian are always? - Correct Answers
-orthonormal sets (i.e. they're orthogonal and normalized)
what is an expectation value? - Correct Answers -for an observatble corresponding to a
quantum mechanical operator (A) in the state described by Ψ,
<A>=INTEGRAL(Ψ*AΨ dT)
de Broglie postulated that the wavelength of a particle is inversely proportional to it's
momentum. The constant of proportionality is? - Correct Answers -h
because nuclear motions are much slower than those ot the electrion, the molecular
Schrodinger equation for electron motion can be solved by assuming that the nuclei are
at fixed locations. This is? - Correct Answers -the Born-Oppenheimer approximation
QUANTUM MECHANICS FINAL EXAM
who assumed the energy of all oscillators in a blackbody was quantized? what was it
said to be quantized by? - Correct Answers -Planck; e=nhv where n=quantum number,
h=Planks constant, and v=frequency of the oscillator
what did Einstein propose through use of Plank's quantization of energy theory? -
Correct Answers -that radiation itself existed as packets of energy (called photons) with
e=hv
what is the empirical equation explaining the observed spectrum of hydrogen? - Correct
Answers -v=Rh((1/n1^2)-(1/n2^2)) where Rh is the Rydberg constant, and n1 and n2
are quantum numbers
the angular momentum of the hydrogen atom is quantized by units of what? - Correct
Answers -h/2Pi or hbar
what is the relation of momentum to wavelength? (de Broglie relation) - Correct
Answers -wavelength=h/p or h/m*v
where v is velocity, m is mass, and h is planck's constant
what is the Schrodinger equation? - Correct Answers -a partial differential equation
describing the wave properties of matter. solutions are called wave functions.
equation for the theory that two electrons cannot occupy the same spatial orbital unless
they are of opposite spin? (Pauli exclusion principle) - Correct Answers -Ψ(1,2)= -Ψ(2,1)
what is the equation for the Heisengburg uncertainty principle? - Correct Answers -ΔxΔp
is greater than or equal to 0.5hbar
what does the correspondence principle state? - Correct Answers -classical and
quantum mechanical results merge in the limit of high quantum numbers
What is the time independent schrodinger equation? - Correct Answers -HΨ=EΨ where
H is the hamiltonian operator and E is the energy
, when is a function an eigen function? - Correct Answers -example: A is an eigen
function if applying A to the function f is the same as the multiplication of f by a constant,
a. Or Af=af
the wavefunctions and energies of systems are _____ of the Hamiltonian operator -
Correct Answers -eigen functions. In other words, applying the Hamiltonian to the wave
function is the same as multiplying the wavefunction by the constant, E or energy.
what is an operator? - Correct Answers -A rule for changing one function into another
function
what makes an operator linear? - Correct Answers -it (represented by A) satisfies the
equation: A(cf+dg)=Acf+Adg where f and g are functions and c and d are constants
what makes an operator Hermitian? - Correct Answers -it (represented by A) satisfies
the equation: INTEGRAL(fAg dT) = INTEGRAL(gAf dT)
what is the Born-Oppenheimer approximation? - Correct Answers -because the
electrons in molecules move much more quickly than the nucleus, we assume the
nucleus is fixed
what is the Fanck-Condon principle? - Correct Answers -because nuclei are much more
massive than electrons, en electronic transition takes place in the presence of a fixed
nucleus
why isn't every solution to the Schrondinger equation acceptable? - Correct Answers -
because of boundary conditions for each given problem. Also, the wave function must
be continuous, continually differentiablex, single-valued (i.e. can't have 2 possible Y
values for one X value), finite-valued (i.e. can't go to infinity), and able to be normalized
over the appropriate range
when a set is orthogonal what happens? - Correct Answers -INTEGRAL(Ψ*Ψ dT)=0
wave functions that are solutions to a given Hamiltonian are always? - Correct Answers
-orthonormal sets (i.e. they're orthogonal and normalized)
what is an expectation value? - Correct Answers -for an observatble corresponding to a
quantum mechanical operator (A) in the state described by Ψ,
<A>=INTEGRAL(Ψ*AΨ dT)
de Broglie postulated that the wavelength of a particle is inversely proportional to it's
momentum. The constant of proportionality is? - Correct Answers -h
because nuclear motions are much slower than those ot the electrion, the molecular
Schrodinger equation for electron motion can be solved by assuming that the nuclei are
at fixed locations. This is? - Correct Answers -the Born-Oppenheimer approximation
