1. After an electron undergoes a n to π² or π to π² transition, what are three ways we discussed it will “relax” or “lose this excess energy”?

2. And what determines if a transition such as those described in question 1 will take place? (another way to ask this might be, why don’t other bond types also undergo a transition – or, do they?).

1. Calculate the probability of locating an electron in a one-dimensional box of length 2.00 nm and n_x=4 between 0 and 0.286 nm. The probability is also plotted. You should compare (qualitatively) your numerical answer to the area under the curve on the graph that corresponds to the probability.

Calculate the moments of inertia (about any axis through the center) for a spherical shell and a solid sphere. What is the ratio between the two moments of inertia. Both spherical shell and solid sphere have mass M, radius R, and uniform mass densities (σ and ρ respectively).

A 0.5-kg mass is attached to a spring with spring constant 2.5 N/m. The spring experiences friction, which acts as a force opposite and proportional to the velocity, with magnitude 2 N for every m/s of velocity. The spring is stretched 1 meter and then released.

(a) Find a formula for the position of the mass as a function of time.

(b) How much time does it take the mass to complete one oscillation (to pass the equilibrium point, bounce back, and return traveling in the same direction)? 1

(c) By what fraction has the amplitude of the motion decreased in this time?

(d) Do the answers to (b) and (c) depend on the initial position of the mass? Why or why not?

(e) By immersing the spring in one of a variety of rare, delicious syrups, it’s possible to increase the damping constant while keeping the spring constant the same. Can you increase the damping constant so that the spring doesn’t oscillate at all, but just returns to its starting point? What’s the smallest value of the damping constant that will do this?

A dose of 3000cGy is delivered to a depth of 8cm where the percent depth dose is 76%. What is the dose to an underlying organ at 14cm depth where the percent depth dose is 58%? The dose at 14cm depth should be lower than the dose at 8cm for two main reasons - briefly explain these reasons.

You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 32˚ when in air? (b) What would the critical angle be for this substance when submerged in water?

1. Oil efficiency and national security. Right now, the United States is extremely dependent on oil for its automobile. Our dependence on oil has turned the Middle East into one of the most important areas in the world. If our automobiles were 40% efficient rather than 20% efficient, we would not have to import any oil. The global consequences of our oil inefficiency can reach as far as war in the Middle East. Getting more efficient use of oil is both a technological and a social issue. Who should pay for the research? The U.S. government? Private industry? Is this an economic question or is it a national security one?
2. Automobiles typically carry 100lb of gasoline. That has the energy content of 1500 lb of TNT. Is gasoline really as dangerous as this makes it sound? If so, why do we accept it in our automobiles? If not, why not? Do we accept gasoline only because it is a “known” evil?

- List three differences between the Sun’s core and the photosphere.

- Describe how sunspots are produced.

- Summarize in words the three steps in the proton-proton chain. Explain why energy is produced when hydrogen fuses into helium using Einstein’s E = mc² equation.

A ladder having a uniform density and a mass m rests against a frictionless vertical wall, making angle 48.0° with the horizontal. The lower end rests on a flat surface where the coefficient of static friction is µ_s = 0.370. A window cleaner with mass M = 2m attempts to climb the ladder. Given a ladder length of L, what fraction of the length of the ladder (x / L) will the worker have reached when the ladder begins to slip?

At time t = 9 sec, a particle of mass M = 3 kg is at the position (x,y,z) = (4,4,6) m and has velocity (2,1,-2) m/s.

1) What is the x component of the particle's angular momentum about the origin?

2) What is the y component of the particle's angular momentum about the origin?

3) What is the z component of the particle's angular momentum about the origin?

4) Now an identical particle is placed at (x,y,z) = (-4,-4,-6) m, with velocity (-2,-1,2) m/s. What is the x component of the pair's total angular momentum about the origin?

5) What is the y component of the pair's total angular momentum about the origin?

6) What is the z component of the pairs's total angular momentum about the origin?

7) Finally a thin rod of mass 9 kg is added between the two particles Since the particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass. What the angular frequency of rotation of the rod + particles system? (Note: The particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass.)

8) What is the magnitude of the total angular momentum of the system (particles plus rod)?

Gamma Ray Absorption

A gamma ray with energy E, hits a stationary nucleus of mass M and is completely absorbed. In terms of E, and M, find expressions for the following quantities.

a. The momentum of the nucleus after absorbing the gamma

b. The total relativistic energy of the nucleus after absorbing the gamma

c. The rest mass energy of the nucleus after absorbing the gamma

d. The kinetic energy of the nucleus after absorbing the gamma

Why do the voltage and current in the pickup coil cycle between negative and positive? Explain in detail using Faraday’s Law. Remember, Lenz’s Law is part of Faraday’s Law! Although it will not be covered explicitly in this class, this is known as alternating current.

a. How the magnetic flux through the loop changes as the magnet rotates (is the flux maximal when the magnet is horizontal or vertical on the screen? Why?)

b. How this changing magnetic flux works to create an emf (potential difference) in the coil which alternates over time (use the Faraday’s law equation)

What is the magnitude of the electric field at a point midway between a −6.5μC and a +5.0μC charge 10cm apart? Assume no other charges are nearby. Express your answer using two significant figures.

What is the magnitude of the force a +20 μC charge exerts on a +3.3 mC charge 39 cm away?

View the video "The Apple and the Moon," video 8 from  The Mechanical Universe and Beyond. In your own words describe Newton's three laws of motion. Give an example that illustrates each law. What are the four fundamental forces of nature? How do these force related to the forces which we may encounter in every day life (string forces, contact forces, spring forces, frictional forces)? How do the three laws of motion differ from Newton's other great achievement the Universal Law of Gravitation?   

There are two identical, positively charged conducting spheres fixed in space. The spheres are 34.8 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0765 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2 . Using this information, find the initial charge on each sphere, ?1 and ?2 , if ?1 is initially less than ?2 . find q1 and q2.