Three discrete spectral lines occur at angles of 10.1°, 13.9°,and 14.6°, respect

Question

Three discrete spectral lines occur at angles of 10.1°, 13.9°,and 14.6°, respectively, in thefirst-order spectrum of a diffraction grating spectrometer. (a) If the grating has 3715 slits/cm, what are the wavelengths of thelight? 1 = 1 nm (10.1°) 2 = 2 nm (13.9°) 3 = 3 nm (14.6°)
(b) At what angles are these lines found in the second-orderspectra? = 4° (1) = 5° (2) = 6° (3)
(a) If the grating has 3715 slits/cm, what are the wavelengths of thelight? 1 = 1 nm (10.1°) 2 = 2 nm (13.9°) 3 = 3 nm (14.6°)
(b) At what angles are these lines found in the second-orderspectra? = 4° (1) = 5° (2) = 6° (3)
1 = 1 nm (10.1°) 2 = 2 nm (13.9°) 3 = 3 nm (14.6°)

Explanation / Answer

d = 1/3715 cm, a) use dsin = 1 = (1/3715)sin(10.1) cm = 472 nm 2 = (1/3715)sin(13.9) cm = 647 nm 3 = (1/3715)sin(14.6) cm = 679 nm b) use dsin = 2 for 1: =sin-1(21/d) = 20.7ofor2: =sin-1(22/d) = 29.0o for 3: =sin-1(23/d) = 30.6o

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