Three discrete spectral lines occur at angles of 10.3°, 13.6°,and 15.0°, respect

Question

Three discrete spectral lines occur at angles of 10.3°, 13.6°,and 15.0°, respectively, in thefirst-order spectrum of a diffraction grating spectrometer. (a) If the grating has 3775 slits/cm, what are the wavelengths of thelight? 1 = 1 nm (10.3°) 2 = 2 nm (13.6°) 3 = 3 nm (15.0°)
(b) At what angles are these lines found in the second-orderspectra? = 4° (1) = 5° (2) = 6° (3)
(a) If the grating has 3775 slits/cm, what are the wavelengths of thelight? 1 = 1 nm (10.3°) 2 = 2 nm (13.6°) 3 = 3 nm (15.0°)
(b) At what angles are these lines found in the second-orderspectra? = 4° (1) = 5° (2) = 6° (3)
1 = 1 nm (10.3°) 2 = 2 nm (13.6°) 3 = 3 nm (15.0°)

Explanation / Answer

1 = 10.3°,2 = 13.6°,3 = 15.0°, a) d = 1/3775 cm = 107/3775 nm dsink = k 1 = dsin1 = 474 nm 2 = dsin2 = 623 nm 3 = dsin3 = 686 nm b) dsink' =2kdsink' =2dsink k' =sin-1(2sink) 1' = sin-1(2sin1) =21.0o 2' = sin-1(2sin2) =28.1o 3' = sin-1(2sin3) =31.2o

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