PhysicsLAB: 1998 B7

A transmission diffraction grating with 600 Iines/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_red = 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 E_n = -13.6/n² eV, where n is an integer designating each successive level. On the energy level diagram provided below, calculate and label the energies for the first four energy levels.

	(c) 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. Show you calculations below. Finally, draw an arrow on the diagram completed above to illustrate the electron's de-excitation.

	(d) Quantitatively 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.