Quantum Mechanics Exam 1

just the essay qs

when is it best to use Newton’s EOM

F=ma

-when you need to know force

-for stuff moving in a straight line

when is it best to Lagrange’s EOM

L = K-V

-use energies

-can work in non-straight lines

-when you need angular momentum (not a useful quantity)

when is it best to use Hamilton’s EOM

H = K(x dot) + V(x)

-use energies

-can work in non-straight lines

-H represents the total energy (useful)

structure of the H-atom: what is it, why classical mechanics fails for it, how people attempted to solve it, and why this lead scientists to belive matter/light has wave-particle duality

-what: how a molecule is stable

-why failed: electron would lose energy as it accelerates in its orbit and spiral into the nucleus, causing it to explode. plus it would allow for any orbit to exist

-solve attempt: bohr model for atom structure, but only works for hydrogen (also isn’t a correct model)

-wave-particle duality: bohr used planck’s energy of the wave in solution, which again proved light could act a particle, as well as electrons acting like a wave in the orbit

spectrum of H-atom: what is it, why classical mechanics fails for it, how people attempted to solve it, and why this lead scientists to belive matter/light has wave-particle duality

-what: light is missing from prisms (absorption and emission)

-why fail: classical says all colors should come back, but colors are missing. why do specific colors should up for elements

-solve attempts: rydberg equation (explained wavelengths from spectra - only works for hydrogen), bohr model

-w/p duality: light is wave, but light is chunk

black-body radiation and UV catastrophe: what is it, why classical mechanics fails for it, how people attempted to solve it, and why this lead scientists to belive matter/light has wave-particle duality

-what: all things with temp give off light

-why fail: in theory, UV catastrophe (as intensity increases, lambda goes to infinity) instead of the smooth curve that goes up and comes back down like we observe

-solve attempt: wein displacement law + Planck’s energy of photon (E=hv)

-w/p duality: light acts as chunks (photons) for energy but we know light is a wave

photoelectric effect: what is it, why classical mechanics fails for it, how people attempted to solve it, and why this lead scientists to belive matter/light has wave-particle duality

-what: as a metal gets excited by a light shining on it, it loses electrons

-why fail: why do you need a minimum/specific amount of frequency to kick out an e- and why is the KE th exact frequency as the light that came in

-solve attempt: Einstein’s equation (plotting Planck’s equation as a straight line) - proves very specific energy connects electron to metal

-w/p duality: confirmed planck’s theory that light is chunk (photons), light is wave

assumptions of Bohr model

1. electrons orbit in circular orbits. orbit is stable bc the coloumbic force is balanced by centrifugal force

2. energy of e- remains constant

3. only certain orbits are allowed

4. transitions between orbits are allowed but only when the e- either absorbs or emits exactly that amount of energy

3 postulates of quantum mechanics

1. the behavior of a quantum system (i.e. e-) can be described by a mathematical wavefunction, psi. all info about the system is contained in psi

2. all observables (o) have a corresponding operator

3. the only possible observable value that can be obtained in a single measurement are the eigenvalues of the operator and the wavefunction

what makes a valid wavefunction

1. must be single valued

2. must be continuous

3. must be differentiable

4. must be bounded (doesn’t go to infinity in the region where the particle lives)

what is the bohr model

model of the H-atom that accounts for how it stays stable