Explain why the classical theory of light as an electromagnetic wave (or of electrons as particles) is unable to explain the following phenomena whereas quantum mechanics is successful.

1. (1) The turn-on voltage of differently colored LEDs

2. (2) The existence of transparent conductors

3. (3) The decrease in frequency of photons scattered off of atoms

4. (4) The spectrum of blackbody emission

For each, use 2-3 sentences, 1-2 equations, and a diagram to provide an explanation that is concise yet precise.

Your kid brother gets a noise emitting toy for Christmas. This toy emits sound at a constant frequency. He attaches the toy to a rope and starts to swing it back and forth. He is facing you. You, seated on the sofa and very annoyed, measure the frequency of the sound as oscillating between 600.0 Hz and 617.75 Hz. Every 2.00 seconds, you hear the sound at the higher frequency. The speed of sound in air is 343 m/s.

(a) What is the toy’s maximum speed? Where does it have this speed?

(b) What is the length of the rope that the toy is attached to?

(c) What is the maximum height the toy reaches?

(d) Far in the future, a young Martian plays with a similar toy on a terraformed Mars. How many seconds are there between the high frequency sounds?

Show that momentum conservation follows from translational invariance.

79. Describe the event types in annihilation coincidence detection and how we correct for non-true coincidence.

I.4. Hartree–Fock approximation. The Hartree–Fock approximation is a simple yet
important model for understanding electron–electron interaction in crystals.
(a) Derive the Hartree–Fock self-consistent field equations from the variational principle
using a Slater determinant of single-particle orbitals as a trial many-electron
wavefunction.
(b) Consider the total electronic energy of a system (e.g. a molecule) in the Hartree–
Fock approximation. Calculate the change in the energy of the system if an
electron is promoted from an occupied ith orbital to an unoccupied jth orbital,
assuming that the orbitals are unchanged after the excitation. How is this excitation
energy related to the eigenvalues of the Hartree–Fock equations? This kind
of excitation is called a neutral excitation, which occurs for example in a photoexcitation
process, since no electrons are added or removed from the system. The
result is known as Koopmans’ theorem.

1. Considering the following data for fluorescent and incandescent bulbs to answer the following questions:

Data from several source: Amazon.

1. Estimate the 2018 energy savings potential on a national scale of replacing all incandescent bulbs in home (residential) with the new energy efficient fluorescent bulbs. Consider that in 2018, total US energy consumption was 101.3 quadrillion British thermal units (Btu). Electricity consumption for all applications amounts for 13 quads, and residential is 11.9% of all electricity consumption in US. Assume that all energy consumption for residential lightning is due to incandescent bulbs and that all those are replaced by fluorescent bulbs. How large are energy savings compared to annual US energy and electricity consumption? State your answer on a percentage basis.

(8 points)

2. From a LCA perspective, define a functional unit and equivalence for this comparison of fluorescent and incandescent bulbs. How many incandescent bulbs are needed to equal one fluorescent bulb? Comment your results. (4 points)
3. Develop an inventory of costs over the life cycle for each bulb type. Compare cost over the life cycle for fluorescent bulbs vs. incandescent bulbs. Which stage of the life cycle accounts for the greatest cost to the consumer? (8 points)

(Total: 20 points)

4. NOTE: be careful with unit conversion, purposely the information comes in a mix of units.

A space station is approximately a ring of radius,R, and mass m, which rotates about its symmetry axis with angular velocity,~ω=ω0ˆe3. A meteor is traveling with momentum,~p, that is parallel to the original ˆe3, and strikes the space station at a point on the rim,transferring the entire momentum to the space station (an inelastic collision where the meteor sticks to the space station). Further, though the meteor has significant momentum,it is of very small mass so that the moment of inertia tensor elements are approximately the same before and after the collision

a) What is the vector angular momentum of the space station with respect to a coordinate system with origin at the center of the ring and one axis along ˆe3 just before the collision?

b) What is the vector angular momentum of the space station in the same coordinate system (and defining the ˆe2 axis as in the direction from the origin to the point of impact on the edge of the ring) just after the collision?

c) After the collision, there are no further torques acting on the space station. Assume that the angular momentum of the space station after the collision differs by only a small (vector) amount from the initial angular momentum. Write down equations of motion that describe how the components of~ωfor the space station evolve with time.

d) Use these equations to describe how the rotational velocity vector of the space station evolves with time. If you predict simple rotation about a new direction, say so and describe the new direction. If you predict precessional motion, say so and predict the precession frequency. If you think something else happens, say so and describe the motion. In all cases, Explain: Back up your prediction with reasoning and (possibly approximate) solutions of the equations from part (c).

A potential difference of 4.50 kV is established between parallel plates in air.

If the air becomes ionized (and hence electrically conducting) when the electric field exceeds 3.05×10⁶ V/m , what is the minimum separation the plates can have without ionizing the air?

Answer in mm.

(a) How much work is required to compress 4.92 mol of air at 19.9

Briefly explain the two postulates of relativity, how they differed from classical physics, and

why Einstein was led to propose them. List at least 2 implications of the postulates.

How to find the central pressure of Jupiter? Assuming we know the mass of the Jupiter.

What is light? You can start by describing the different historic models for light and explain their individual strength and shortcomings in explaining observable phenomena. Then, try to summarize our current quantum mechanic understanding and highlight its implications for all matter and energy. Finally, consider identifying visible light within the electromagnetic (EM) spectrum and discuss applications that may depend on different light effects such as photoelectric or electro-luminescent effect.