Back-of-the-envelope CO: It is well-known (certainly among astronomers) that the Einstein A-coefficient for the Lyman alpha (n = 2 to n = 1) transition in atomic hydrogen is of order 10^9 s^−1 (actually, 5 × 10^8 s^−1). As we briefly discussed in class, this result could be estimated to order-of-magnitude by considering an (accelerating) electron on a spring that displaces a Bohr radius, a0, and has natural angular frequency ω and then taking the inverse lifetime of the excited state as A ∼ P/ω, where P is the power radiated by an accelerating charge. The ubiquitous carbon monoxide molecule, 12CO, is used by astronomers to trace the presence and measure the temperature of molecular gas in various astrophysical environments. We would rather try to detect H2 directly, but sadly H2 has no permanent electric dipole moment because of its symmetry, while Carbon monoxide does have a permanent dipole moment, so is easier to detect.

a)Estimate the wavelength of the lowest energy, rotational transition in CO (J = 1 to J = 0, where J is the rotational quantum number). Do this by considering a barbell spinning about its axis of greatest moment of inertia and recognizing that angular momentum comes quantized in units of ?h. Compare your estimate
to the true answer of 2.6 mm.

b)Use scaling relations to estimate the Einstein A coefficient of this transition, i.e., the inverse lifetime of the excited J = 1 state. You can use that the dipole moment (that is difficult to guess from first principles) of the CO molecule is 0.1 Debyes, not ∼ 1 Debye, as one might have guessed naively (1 Debye= 10^−18cgs. Note that ea0 = 2.5 Debyes, where e is the electron charge). Compare your estimate to the true answer A10 = 7.4 × 10^-8 s^-1.

Note: This smaller-than-expected dipole moment of CO is a consequence of the strong double bond connecting C to O. Most other molecules common in astrophysics – e.g., H2O, CS, SiS, SiO, HCN, OCS, HC3N – have dipole moments that are all of order 1 Debye.

Use the Bohr model to calculate the radius, in angstroms, of an He+ ion with an electron in the n=4 state.

r=

Å

Calculate the energy, in joules, of an He+ ion with an electron in the n=4 state.

E=

J

How much energy would be required to completely remove the electrons from 1.48 mol of He+ ions in the n=4 state?

energy to remove electrons:

J

What wavelength of light would be emitted in a transition from the n=4n=4 state to the n=2n=2 state of an He+He+ ion?

λ=λ=

m

What frequency of light would be emitted in a transition from the n=4 state to the n=2 state of an He+ ion?

ν=

Hz

1. NASA tested a power generation system that involves connecting a small satellite to the space shuttle with a conductive wire several kilometers long. Explain how such a system can generate electricity.
2. The use of high-voltage lines in homes (for example, 600 V or 1,200 V) would reduce energy waste. Why are they not used?
3. What parameters affect the inductance of a coil? Does the inductance of a coil depend on the current in it?
4. How does resistance, capacitive reactance and inductive reactance change, when the frequency in a circuit is increased?
5. Does the phase angle depend on the frequency? What is the phase angle when the inductive reactance is equal to the capacitive reactance?

a.) M, a solid cylinder (M=2.11 kg, R=0.137 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.610 kg mass, i.e., F = 5.984 N. Calculate the angular acceleration of the cylinder. a.)

b.) If instead of the force F an actual mass m = 0.610 kg is hung from the string, find the angular acceleration of the cylinder.

c.) How far does m travel downward between 0.590 s and 0.790 s after the motion begins?

d.) The cylinder is changed to one with the same mass and radius, but a different moment of inertia. Starting from rest, the mass now moves a distance 0.328 m in a time of 0.490 s. Find I_cm of the new cylinder.

A farmer uses a tractor to pull a 190 kg bale of hay up a 15∘ incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.45.

What is the tractor's power output?

What mass of ice at -10.5°C is needed to cool a whale's water tank, holding 1.13 103 m3 of water, from 20.0°C down to a more comfortable 10.0°C?

At t = 0, one toy car is set rolling on a straight track with initial position 14.0 cm, initial velocity -3 cm/s, and constant acceleration 2.30 cm/s². At the same moment, another toy car is set rolling on an adjacent track with initial position 8.5 cm, initial velocity 6.00 cm/s, and constant zero acceleration.

(a) At what time, if any, do the two cars have equal speeds? (Enter NA if the cars never have equal speeds.)


(b) What are their speeds at that time? (Enter NA if the cars never have equal speeds.)
cm/s

(c) At what time(s), if any, do the cars pass each other? (If there is only one time, enter NA in the second blank. If there are two times, enter the smaller time first. If they never pass, enter NA in both blanks.)



(d) What are their locations at that time? (If there is only one position, enter NA in the second blank. If there are two positions, enter the smaller position first. If they never pass, enter NA in both blanks.)




(e) Explain the difference between question (a) and question (c) as clearly as possible.

Three moles of an ideal monatomic gas expand at a constant pressure of 2.10 atm ; the volume of the gas changes from 3.30×10−2 m3 to 4.50×10−2 m3 .

a) Calculate the initial temperature of the gas.

b) Calculate the final temperature of the gas.

c) Calculate the amount of work the gas does in expanding.

d) Calculate the amount of heat added to the gas.

e) Calculate the change in internal energy of the gas

Ch 19

8. A nearsighted person has glasses with a prescription of -6.25 D. What is the farthest he can see clearly without corrective lenses (far-point)? 16 cm

9. A farsighted person has a near-point of 75 cm. What prescription should his glasses have to bring his near-point to 25 cm? 2.67 D

10. A person with a far point of only 25 cm wants glasses that he can wear while using a computer monitor 65 cm away from his eyes. What refractive power do these glasses require? -2.46 D

11. A 2 cm tall object is projected as a 8 cm tall real image.

a) What is the focal length of the lens if the object is 5 cm from the lens? 4 cm

b) Is the lens convex or concave? Convex

a boy pulls his 6.35kg sled 5m across a patch of ice where the sled accelerates at a=0.39m/s^2. He pulls the sled by a rope with tension 10.6N at an angle of 30 degrees above the horizontal. (a) Find the work done by each force. (b) Find the net work

your ear canal has a resonant frequency in the region around 3000hz，

compute the length of your ear canal with the above assumption，and sketch a diagram showing the resonant .

make sure the answer makes physical sense

a 1.25kg mass on a pring vibrates as simple harmonic oscillator with time dependant position y, y(t)=(0.250m)vos(12.1t)
find:
a. amplitude im meter
b.frequency of oscillation in hertz
c.period of osillation in s
d.position at t=1.4s
e.velocity at t=1.4s
f.spring constant k