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Diffraction grating problem?
Three discrete spectral lines occur at angles of 10.2°, 13.6°, and 14.8°, respectively, in the first-order spectrum of a diffraction grating spectrometer.
(a) If the grating has 3720 slits/cm, what are the wavelengths of the light?
I got 542 nm for the first angle, and 703 for the second but my homework website is saying that I'm wrong. I did some problems that had different numbers and I got it right, so I don't know if I'm typing my numbers wrong or something but I am just not getting the right answer. Can somebody verify before I ask my teacher if the answers are correct? Thanks!
2 Answers
- kuiperbelt2003Lv 71 decade agoFavorite Answer
the relevant equation is
d sin(theta) = n lambda
if n=1 in all cases, and d=1/3720cm=2.7x10^(-6), we have
2.7x10^(-6) sin 10.2=476nm
for the second angle,
2.7x10^(-6) sin 13.6=632nm
finally,
2.7x10^(-6) sin 14.8 = 687nm
