The hydrogen spectrum includes a red line at 656 nm and a blue-violet line at 43

Question

The hydrogen spectrum includes a red line at 656 nm and a blue-violet line at 434 nm. What are the angular separations between these two spectral lines for all visible orders obtained with a diffraction grating that has 5 000 grooves/cm? (In this problem assume that the light is incident normally on the gratings.) first order separation Incorrect: Your answer is incorrect. The angular separation is the difference between the angles of the two spectral lines. ° second order separation Incorrect: Your answer is incorrect. How do you calculate the angle of the line for a particular wavelength in the second order spectrum? ° third order separation

Explanation / Answer

angle of spectral line is b=asin(n*/d), where
1/d = 5000 grooves/cm = 5.0e5 grooves/m;
angular separation of order n is
b = b1-b2 = asin(n*1/d) - asin(n*2/d), where
1=656e-9 m, 2=434e-9 m;
(a) n=1; b = asin(656e-9*5.0e5) - asin(434e-9*5.0e5) =0.111°;
(b) n=2; b = asin(2*656e-9*5.0e5) - asin(2*434e-9*5.0e5) =0.222°;

(c) n=2; b = asin(3*656e-9*5.0e5) - asin(3*434e-9*5.0e5) =0.333°;

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