1998B7 (10 points) A transmission diffraction grating with 600 lines/mm is used

Question

1998B7 (10 points) A transmission diffraction grating with 600 lines/mm is used to study the line spectrum of the light produced by a hydrogen discharge tube with the setup shown above. The grating is 1.0 m from the source (a hole at the center of the meter stick). An observer sees the first-order red line at a distance yr = 428 mm from the hole. a. Calculate the wavelength of the red line in the hydrogen spectrum. b. According to the Bohr model, the energy levels of the hydrogen atom are given by En = -13.6 eV/n^2 , where n is an integer labeling the levels. The red line is a transition to a final level with n = 2. Use the Bohr model to determine the value of n for the initial level of the transition. c. Qualitatively describe how the location of the first-order red line would change if a diffraction grating with 800 lines/mm were used instead of one with 600 lines/mm.

Explanation / Answer

The number of lines on the grating is N = 600 lines/mm The distance of the grating to the screen is d = 1 m The distance of the firdt order red line from the center is y = 428 nm The slit seperation of the grating is d = 1/N = 1.67*10-3 mm The diffratcion condition is y = mD/d is the wavelengt of the light used a) 428*10-3 mm = (1)()(1 m)/(1.67*10-6 mm) = 7.15*10-7 m = 715 nm b) The energy of the transition is E = -13.6 eV/n2 The energy released/absorbed is E = -13.6 eV/n22 + 13.6 eV/n12 therefore hc/ = -13.6 eV/n22 + 13.6 eV/n12 (6.63*10-34 Js)(3*108 m/s)/715 nm = -13.6 eV/22 + 13.6 eV/n12 (6.63*10-34 Js)(3*108 m/s)/715 nm = -13.6 eV/22 + 13.6 eV/n12 n1 ˜ 1 c) Clearly the seperation from the center is inversely prportional to the slit width which inturn varies with number  of lines on the grating As the number of lines increased, the slit width decreases and increment in the seperation from the center

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.