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Name:
Student #
- For credit: Please redo only 2 problems between 1 through 6.
- For extra credit: You may do the one of problems 7, 8, or 9 which you did not do in the regular test.
- Indicate below which problems you have done.
My redo problems are:
PHY215, fall 2006
Modern Physics and Thermodynamics
Exam #2, Round Two. Due Monday, November 13, 2006
Please show all of your work. If you need more space, use the back and indicate clearly what problem is being continued. If you still need more space...ask for another sheet and clearly include your name and what problem is begin continued.
Constants
1 calorie = 4.186 J 1 atmosphere = 1. 01 × 105 Pa Gas Constant: R = 8. 3145 J/mol·K Bolzmann's Constant: k = 1. 38 × 10 −^23 J/L Sefan-Boltzmann's constant: σ = 5. 67 × 10 −^8 W/m^2 K^4 Avagadro's Number: NA = 6. 023 × 1023 mol−^1 Speed of Light: c = 3 × 108 m/s Charge of the electron: −e = − 1. 6 × 10 −^19 C Mass of the electron: me = 9. 1094 × 10 −^31 kg = 511 keV/c^2 Mass of the proton: mp = 1. 6726 × 10 −^27 kg = 938. 3 MeV/c^2 Mass of the neutron: mn = 1. 6749 × 10 −^27 kg = 939. 6 keV/c^2 Mass of the alpha particle: mα = 3727. 4 MeV/c^2 Planck's Constant: h = 6. 63 × 10 −^34 J-s = 4. 14 × 10 −^15 eV-s ...times c: hc = 1. 9864 × 10 −^25 J-m = 1239. 8 eV-nm Reduced h: h/ 2 π = ¯h = 1. 0546 × 10 −^34 J-s = 6. 5821 × 10 −^16 ev-s ...times c: ¯hc = 3. 162 × 10 −^28 J-m = 197. 33 eV-nm
Electrostatic constant:
4 π 0
= 8. 9876 × 109 N-m^2 -C−^2
...times e^2 :
e^2 4 π 0
= 2. 3071 × 10 −^28 J-m = 1. 4400 × 10 −^9 eV-m
Bohr radius: a 0 =
¯h mecα
= 0. 5292 × 10 −^10 m
Fine structure constant: α = e^2 4 π 0 ¯hc
- (5 pts) Thomson's "Plum Pudding" model of the atom imagined a pudding of positive charge interspersed with "plums" of particulate electrons. It could not explain what experiment done by his old student, Rutherford, and why? A sketch might help.
- (total for problem: 10 pts) The cosmic ray particle, the muon (μ) has a rest energy of 106 MeV. It can be produced in the lab and actually be captured by a proton to form a muonic atom in which the μ takes the place of an electron in an otherwise hydrogen-looking atom. So, the bound system is one of proton-muon. a. (2 pts) Show that the reduced mass of the μ − p system is 95.2 MeV/c^2.
b. (5 pt) What is the smallest radius for the orbiting muon according to the Bohr model?
c. (3 pts) What is the binding energy of the muon-proton system in the lowest Bohr orbit compared to that of normal hydrogen atom?
- (total for problem: 10 pts) A wavefunction has the value ψ = A sin x between 0 and 2 π and zero elsewhere. a. (5 pts) What is the normalization constant, A?
b. (5 pts) Sketch the wavefunction and the probability density on the same graph. don't worry about an absolute vertical scale, but show the relative sizes of the two curves in your sketch.
- (total for problem: 10 pts) A electron moves with a speed of v = 10−^4 c inside a one-dimensional box of length 48.5 nm. The potential is zero elsewhere and the electron may not escape the box. a. (3 pts) Treating the electron as nonrelativistic, show that its kinetic energy is E = 0. 002555 eV.
b. (7 pts) What is the approximate quantum number of the electron?
- (5 pts) White dwarf stars have been observed with a surface temperature as hot as 200 , 000 ◦C. What is the wavelength of the maximum intensity produced by the star?
- (5 pts) A gamma ray of 700 keV energy Compton-scatters from an electron. Find the energy of the scattered photon at 110 ◦^ and the energy of the scattered electron.
