Three discrete spectral lines occur at angles of 10.4°,13.7°, and 14.8°,respecti

Question

Three discrete spectral lines occur at angles of 10.4°,13.7°, and 14.8°,respectively, in the first-order spectrum of a diffraction gratingspectrometer. (a) If the grating has 3780 slits/cm, what are the wavelengths of thelight? 1 = nm (10.4°) 2 = nm (13.7°) 3 = nm (14.8°)
(b) At what angles are these lines found in the second-orderspectra? = ° (1) = ° (2) = ° (3) (a) If the grating has 3780 slits/cm, what are the wavelengths of thelight? 1 = nm (10.4°) 2 = nm (13.7°) 3 = nm (14.8°)
(b) At what angles are these lines found in the second-orderspectra? = ° (1) = ° (2) = ° (3) 1 = nm (10.4°) 2 = nm (13.7°) 3 = nm (14.8°)

Explanation / Answer

    We have the formula for the wavelength isgiven by           1 = (sin10.4°)/(3780slits/cm)             2 = (sin13.7°)/(3780slits/cm)           3 = (sin14.8°)/(3780slits/cm) b) The angles are           1 = sin-1[1(2*3780 slits/cm)]              2 = sin-1[2(2*3780 slits/cm)]              3 = sin-1[3(2*3780 slits/cm)] Simplifying we get the answer.

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