Selected solutions to 221 Exam File

The space and time of relativity
2. 9.4´ 105, 9.9, 1.988
3. 310m, 51m
4. 1300m
Relativistic mechanics
4. 135MeV/c2, 2.22, 0.89c
8. l '=[(1-b)/(1+b)]1/2l, b=0.21, 50fm
Atoms
1. 2.2Mm/s, 9.6´ 107C/kg
3. 4300´ , 0.15m
Quantization of light
1. 900mK
4. 11W
7. 490THz, 610nm, 4.2eV
Quantization of atomic energy levels
1. 68eV
2. -27eV/n3, 4350
3. 0.58mm
4. 3´ 1015
Matter waves
1. 0.0073c
2. 8.3´ 10-36m, 2.5´ 10-35m
3. w=akn+1, n+1, for n>0
4. Nope
5. 8.0eV/c2
6. 2.6´ 10-19eV/c2
7. 6.5´ 10-17s
8. 6.8m/s, 2.0´ 10-36m, 1.1m/s
9. 72keV/c, 17pm, 16%
12. 30mm, 60, 0.3%
13. 10-104s
Schrödinger's Equation: 1D
1. 4.14´ 1016Hz, 0.53A
4. 3´ 1030
10. a=mE/(hbar)2
11. A=8a2(hbar)2/m, B=-6a(hbar)2/m
13. U=E-(hbar)2/mL2(1-x2/L2)
Schrödinger's Equation: 3D
4. 1eV (1), 2eV (3), 3eV (3), 3.7eV (3), 4eV (1), 4.7eV (6), 5.7eV (3), 6eV (3), 6.3eV (3)
5. (2,1,1) or (1,2,1) or (1,1,2), (L/4,L/2,L/2), (3L/4,L/2,L/2) for (2,1,1), etc.
8. 12ao, 3 ao
9. 2(hbar), (hbar), 0; 35, 66, 90, 114, 145; 1.610-22J, 0.810-22J,0
11. D(0)=1.37, D(1)=0.87, E25= -34.3eV
12. E= -(hbar)2a2/2m, U= -2(hbar)2a/mr
14. 0.028G
15. 31° ,149°
Tunneling
1. The higher one
3. exp(-1.71040)