PHYSICAL CHEMISTRY - ACS QUANTUM MECHANICS FINAL EXAM QUESTIONS WITH
CORRECT ANSWERS LATEST UPDATE 2026/2027
who assumed the energy of all oscillators in a blackbody was quantized? what was it said to be
quantized by? - 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? - 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? - 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? - Answers h/2Pi or
hbar
what is the relation of momentum to wavelength? (de Broglie relation) - 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? - 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) - Answers Ψ(1,2)= -Ψ(2,1)
what is the equation for the Heisengburg uncertainty principle? - Answers ΔxΔp is greater than
or equal to 0.5hbar
what does the correspondence principle state? - Answers classical and quantum mechanical
results merge in the limit of high quantum numbers
What is the time independent schrodinger equation? - Answers HΨ=EΨ where H is the
hamiltonian operator and E is the energy
when is a function an eigen function? - 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 - 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? - Answers A rule for changing one function into another function
what makes an operator linear? - 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? - Answers it (represented by A) satisfies the equation:
INTEGRAL(fAg dT) = INTEGRAL(gAf dT)
what is the Born-Oppenheimer approximation? - 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? - 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? - 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? - Answers INTEGRAL(Ψ*Ψ dT)=0
wave functions that are solutions to a given Hamiltonian are always? - Answers orthonormal
sets (i.e. they're orthogonal and normalized)
what is an expectation value? - 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? - 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? - Answers the Born-Oppenheimer approximation
According to the Heisenburg uncertainty priciple, if the operators for two physical properties do
not commute then? - Answers the product of the two uncertainties must be greater than of
equal to h/4Pi or hbar/2
the requirement that wavefunctions for electrons in atoms and molecules be antisymmetric
with respect to interchange of any pair of electrons is? - Answers the Pauli exclusion principle
for electrons emitted due to the photoelectric effect, what are the kinetic energy and current
functions of? - Answers kinetic energy is a function of frequency and current is a function of
intensity
in he Schrodinger equation the quantity H (hamiltonian) represents the? - Answers total energy
operator
the total energy of a particle with mass =m moving in the x-direction with momentum=p is
p^2/2m. The Hamiltonian operator for this system is? - Answers since the operator for
CORRECT ANSWERS LATEST UPDATE 2026/2027
who assumed the energy of all oscillators in a blackbody was quantized? what was it said to be
quantized by? - 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? - 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? - 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? - Answers h/2Pi or
hbar
what is the relation of momentum to wavelength? (de Broglie relation) - 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? - 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) - Answers Ψ(1,2)= -Ψ(2,1)
what is the equation for the Heisengburg uncertainty principle? - Answers ΔxΔp is greater than
or equal to 0.5hbar
what does the correspondence principle state? - Answers classical and quantum mechanical
results merge in the limit of high quantum numbers
What is the time independent schrodinger equation? - Answers HΨ=EΨ where H is the
hamiltonian operator and E is the energy
when is a function an eigen function? - 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 - 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? - Answers A rule for changing one function into another function
what makes an operator linear? - 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? - Answers it (represented by A) satisfies the equation:
INTEGRAL(fAg dT) = INTEGRAL(gAf dT)
what is the Born-Oppenheimer approximation? - 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? - 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? - 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? - Answers INTEGRAL(Ψ*Ψ dT)=0
wave functions that are solutions to a given Hamiltonian are always? - Answers orthonormal
sets (i.e. they're orthogonal and normalized)
what is an expectation value? - 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? - 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? - Answers the Born-Oppenheimer approximation
According to the Heisenburg uncertainty priciple, if the operators for two physical properties do
not commute then? - Answers the product of the two uncertainties must be greater than of
equal to h/4Pi or hbar/2
the requirement that wavefunctions for electrons in atoms and molecules be antisymmetric
with respect to interchange of any pair of electrons is? - Answers the Pauli exclusion principle
for electrons emitted due to the photoelectric effect, what are the kinetic energy and current
functions of? - Answers kinetic energy is a function of frequency and current is a function of
intensity
in he Schrodinger equation the quantity H (hamiltonian) represents the? - Answers total energy
operator
the total energy of a particle with mass =m moving in the x-direction with momentum=p is
p^2/2m. The Hamiltonian operator for this system is? - Answers since the operator for
