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6.A: Photons and Matter Waves Page Title (Answer)

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    10331
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    Check Your Understanding

    6.1. Bunsen’s burner

    6.2. The wavelength of the radiation maximum decreases with increasing temperature.

    6.3. \(T_α/T_β=1/\sqrt{3}≅0.58\), so the star \(β\) is hotter.

    6.4. \(3.3×10^{−19}J\)

    6.5. No, because then \(ΔE/E≈10^{−21}\)

    6.6. \(−0.91 V; 1040 nm\)

    6.7. \(h=6.40×10^{−34}J⋅s=4.0×10^{−15}eV⋅s;−3.5%\)

    6.8. \((Δλ)_{min}=0m\) at a \(0°\) angle; \(71.0pm+0.5λ_c=72.215pm\)

    6.9. 121.5 nm and 91.1 nm; no, these spectral bands are in the ultraviolet

    6.10. \(v_2=1.1×10^6m/s≅0.0036c; L_2=2ℏK_2=3.4eV\)

    6.11. 1.7 pm

    6.12. \(λ=2πna_0=2(3.324Å)=6.648Å\)

    6.13. \(λ=1.417pm; K=261.56keV\)

    6.14. \(0.052°\)

    6.15. doubles it

    Conceptual Questions

    1. yellow

    3. goes from red to violet through the rainbow of colors

    5. would not differ

    7. human eye does not see IR radiation

    9. No

    11. from the slope

    13. Answers may vary

    15. the particle character

    17. Answers may vary

    19. no; yes

    21. no

    23. right angle

    25. no

    27. They are at ground state.

    29. Answers may vary

    31. increase

    33. for larger n

    35. Yes, the excess of 13.6 eV will become kinetic energy of a free electron.

    37. no

    39. X-rays, best resolving power

    41. proton

    43. negligibly small de Broglie’s wavelengths

    45. to avoid collisions with air molecules

    47. Answers may vary

    49. Answers may vary

    51. yes

    53. yes

    Problems

    55. a. 0.81 eV;

    b. \(2.1×10^{23}\);

    c. 2 min 20 sec

    57. a. 7245 K;

    b. 3.62 μm

    59. about 3 K

    61. \(4.835×10^{18}\)Hz; 0.620 Å

    63. 263 nm; no

    65. 369 eV

    67. 4.09 eV

    69. 5.54 eV

    71. a. 1.89 eV;

    b. 459 THz;

    c. 1.21 V

    73. 264 nm; UV

    75. \(1.95×10^6m/s\)

    77. \(1.66×10^{−32}kg⋅m/s\)

    79. 56.21 eV

    81. \(6.63×10^{−23}kg⋅m/s\); 124 keV

    83. 82.9 fm; 15 MeV

    85. (Proof)

    87. \(Δλ_{30}/Δλ_{45}=45.74%\)

    89. 121.5 nm

    91. a. 0.661 eV;

    b. –10.2 eV;

    c. 1.511 eV

    93. 3038 THz

    95. 97.33 nm

    97. a. \(h/π\);

    b. 3.4 eV;

    c. – 6.8 eV;

    d. – 3.4 eV

    99. \(n=4\)

    101. 365 nm; UV

    103. no

    105. 7

    107. 145.5 pm

    109. 20 fm; 9 fm

    111. a. 2.103 eV;

    b. 0.846 nm

    113. 80.9 pm

    115. \(2.21×10^{−20}m/s\)

    117. \(9.929×10^{32}\)

    119. \(γ=1060; 0.00124 fm\)

    121. 24.11 V

    123. a. \(P=2I/c=8.67×10^{−6}N/m^2\);

    b. \(a=PA/m=8.67×10^{−4}m/s^2\);

    c. \(74.91 m/s\)

    125. \(x=4.965\)

    Additional Problems

    127. \(7.124×10^{16}W/m^3\)

    129. 1.034 eV

    131. \(5.93×10^{18}\)

    133. 387.8 nm

    135. a. \(4.02×10^{15}\);

    b. 0.533 mW

    137. a. \(4.02×10^{15}\);

    b. 0.533 mW;

    c. 0.644 mA;

    d. 2.57 ns

    139. a. 0.132 pm;

    b. 9.39 MeV;

    c. 0.047 MeV

    141. a. 2 kJ;

    b. \(1.33×10^{−5}kg⋅m/s\);

    c. \(1.33×10^{−5}N\);

    d. yes

    143. a. 0.003 nm;

    b. \(105.56°\)

    145. \(n=3\)

    147. a. \(a_0/2\);

    b. \(−54.4eV/n^2\);

    c. \(a_0/3,−122.4eV/n^2\)

    149. a. 36;

    b. 18.2 nm;

    c. UV

    151. 396 nm; 5.23 neV

    153. 7.3 keV

    155. 728 m/s; \(1.5μV\)

    157. \(λ=hc/\sqrt{K(2E_0+K)}=3.705nm,K=100keV\)

    159. \(Δλ^{(electron)}_c/Δλ^{(proton)}c_=m_p/m_e=1836\)

    161. (Proof)

    163. \(5.1×10^{17}Hz\).

    Contributors

    Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).