An oscillator with frequency f = 8×1011 hz (about that of a diatomic molecule) is in equilibrium with a thermal reservoir at temperature t. the spacing between the energy levels of the oscillator is given by ε = hf, where h = 6.626×10-34 j*sec.

a)

for what temperature does p1/p0 = 1/2, where p1 is the probability that the oscillator has e = ε (the first excited state) and p0 is the probability that it has e = 0 (the lowest energy state)?

t =

k

b)

if t is 10% of the value you calculated in part 1), what is the ratio p1/p0?

p1 / p0 =

c)

at the temperature of part 2), what is the ratio p2/p1, where p2is the probability that the oscillator is in the second excited state (e = 2ε)?

p2/p1 =

d)

now suppose you have a large number of these oscillators (such as in a solid). at the temperature of parts 2) and 3), what is the average thermal energy per oscillator divided by kt? that is, calculate /kt. (equipartition would have this ratio be 1, but that's not the answer here.)

/ kt =

List one type of erosion and describe how it happens?

Within a pendulum, as potential energy decreases, energy increases. a. heat b. kinetic c. frictional d. gravitational

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?