Physical Chemistry Exam 1

wave particle duality

light and matter behave as both waves and particles

youngs double slit experiment

shows wave interference

photoelectric effect

demonstrates particle nature (photons)

energy of a photon

shorter wavelength → higher energy

longer wavelength → lower energy

particle in a 1D box

energy levels quantized by boundry conditions

particle on a ring

models rotaitonal motion

energy depends on quantum number n

harmonic oscillator

models vibrational motion

quantized equally spaced energy levels

davisson-germer experiment

diffraction of electrons shows wave nature

quantum numbers

derived from bounfry conditions in 3D systems (hydrogen atom)

probability distributions

wave functions describe probabilites, not certainties

probability density

psi squared

gives likelihood of finding a particle in space

rydberg constant

R

13.6eV for hydrogen

radical distribution functions

show probability of finding an electron at distance r

effective nuclear charge

electrons are shielded by inner shells

energy ordering: s < p < d < f

pauli exculsion principle

no two electrons can share the same set of quantum numbers

hunds rule

electrons fill degenerate orbitals singly before pairing

valence bond theory

bonds form by overlap of atomic orbitals

explains hybridization (sp, sp2, sp3)

localized picture

electrons resides between bonded atoms

molecular orbital theory

electrons described by MOs that span the entire molecule

constructive interference

bonding orbital

destructive interference

antibonding orbital

linear combination of atomic orbitals

gives MO diagrams

ex: H2O has bonding, antibonding, and nonbonding orbitals corresponding to lone pairs

quantum mechanics

explains atomic/molecular behavior thorugh wave functions, quantization and probability

atomic structure

governed by quantum numbers, sheilding, penetration and orbital ordering

bonding

described by localized (Vb) vs delocalized (MO) models

both are useful perspectives

explain how the photoelectric effect providdes evidence for the particle nature of light

the photoelectric effect shows light acts like particles because energy transfer depends on photon frequency not intensity

in youngs double slit expirement, electrons are sent through one at a time. why does an interference pattern still emerge over time?

interference pattern emerges because each electron behaves like a wave traveling through both slits, but is detected as a particle #waveparticleduality

compare the de Broglie wavelength of an electron and a baseball (thrown at the same speed). Why is the wave behavior observable in one case but not the other?

the electrons de Broglie wavelength is comparable to atomic scales while the baseballs is unimaginably small so only the electron shows wave behavior

define what is meant by a probability distribution in quantum mechanics

it represents the likelihood of finding a particle in a given region of space

derived from psi squared

why do electrons in a 1D box have quantized energy levels?

boundry conditions restrict allowed wavelengths

only standing waves fit giving quantized energy

how does the length of the box affect the spacing between the energy levels?

a longer box lowers energy spacing since confinement is weaker

when an electron transitions from n=2 to n=1, what determines the wavelength of the emitted photon?

the energy gap via E=hc/lambda

why do higher quantum numbers correspond to wavefunctions with more nodes?

approximates rotational motion of an electron or molecule around a fixed axis

in the particle on a ring model, what physical situation is being approximated?

approximates rotational motion of an electron or molecule around a fixed axis

why do rotational energy levels depend on only one quantum number?

only one boundry condition (cyclic continuity), so one quantum number is needed

explain why the degeneracy of rotational energy levels increases for higher quantum numbers

higher m values yield multiple degenrate states (+m and -m)

what is meant by a cyclic boundry condition in this model?

the wavefunction must repeat after a full 2pi revolution

why does the quantum harmonic oscillator have equally spaced energy levels?

the restoring force is linear in displacement, giving evenly spaced levels

explain why vibrational transitions are usually in the infrared region of the spectrum

vibrational transitions match IR photon energies (thousands of cm^-1)

why is the probability distribution of a high energy vibrational state more concentrated near the turning points?

at a high n, classical turning points dominate, so probability piles up there

in vibrational motion, why can we model bonds as springs?

chemical bonds behave like springs (hookes law approximation)

what are the four quantum numbers and what physical property does each represent?

n: energy

l: shape

ml: orientation

ms: spin

explain the concept of effective nuclear charge and its effect on orbital energy ordering

effective nuclear charge increases across a period, lowering orbital energies

why is the 3s orbital lower in energy than the 3p orbital in many electron atoms?

the 3s orbital penetrates closer to the nucleus, so it feels more nuclear charge and its lower in energy

state the pauli inclusion principle in your own words

no two electrons can share all four quantum numbers

how does the valence bond theory explain the shape of molecules such as methane (CH4)?

VB: sp3 hybrid orbitals explain tetrahedral shape

in molecular orbital theory what is the difference between bonding and antibonding orbitals?

bonding orbitals lower energy

antibonding raise energy

what does it mean when two orbitals combine “constructively” and “destructively”?

constructive overlap increases electron density between nuclei

destructive creates nodes

why do some molecular orbitals remain nonbonding (ex: lone pairs in water)?

some orbitals have symmetry that prevents overlap so they remain nonbonding

compare how valence bond theory and MO theory describe the electron distribution in a molecule.

VB theory localizes bonds

MO theory delocalizes across the whole molecule

in the photoelectric effect why does increasing he intensity of light below the threshold frequency not eject electrons?

below threshold frequency, photons lack sufficient energy to eject electrons no matter the intensity

why does the energy gap between adjacent levels decrease as the quantum number increases?

at higher n, level spacing shrinks because energy infinity n² so difference between adjacent n values decreases relative to energy scale

why do rotational transitions of molecules often fall in the microwave region of the spectrum?

rotational spacings are small (<100cm^-1), matching microwave photon energies

why are vibrational populations at room temperature almost always in the ground state?

vibrational gaps are large (~1000-4000cm^-1), much larger than thermal energy at room temperature so excited states are rarely populated

state hunds rule and its signifigance for electron configurations

hunds rule: in degenerate orbitals, electrons occupy singly with parallel spins before pairing. this minimizes repulsion and stabalizes configuration

compare how valence bond theory and molecular orbital theory describe bonding in O2. which theory better explains paramagnetism?

VB theory: O=O double bond with paired electrons

MO theory: predicts two unpaired electrons in degenerate pi star orbitals (explains paramagnetism)