Note: Figure is drawn to scale. 1. A reflection diffraction grating with 600 lin

Question

Note: Figure is drawn to scale. 1. A reflection 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 y,= 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 n2. 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. 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

   we are given that    slit width a = (1 / 600) x 10-3m    D = 1.00 m    y = 428 x 10-3 m (a)    we get the wavelength from    a sin = m    as the order is the first order thenwe take m = 1     is the angle between the two dottedlines    so solve for (b)    En - E2 = h c /    h c / = (- 13.6 eV /n2) - (- 13.6 eV / 22)    solve for n (c)    the first order red line would beabove the existing dotted line    we are given that    slit width a = (1 / 600) x 10-3m    D = 1.00 m    y = 428 x 10-3 m (a)    we get the wavelength from    a sin = m    as the order is the first order thenwe take m = 1     is the angle between the two dottedlines    so solve for (b)    En - E2 = h c /    h c / = (- 13.6 eV /n2) - (- 13.6 eV / 22)    solve for n (c)    the first order red line would beabove the existing dotted line

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