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°; ±1.6×10-22J, ±0.8×10-22J,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(-1.7×1040)