The hydrogen spectrum has a red line at 656 nm,and a blue line at 434 nm.What is the first order angular separation between the two spectral lines obtained with a diffraction grating with 5000 rulings/cm?
A)7.7$\degree$
B)16.6$\degree$
C)6.6$\degree$
D)3.2$\degree$
E)19.2$\degree$

Question

Quizplus · Accepted Answer

The formula for angular separation of spectral lines produced by a diffraction grating is 
θ = λ/d
where λ is the wavelength of the light, and d is the distance between the rulings on the grating. 
Since the grating has 5000 rulings/cm, the distance between rulings is 
d = 1/5000 cm/ruling = 2 x 10^-4 cm/ruling
For the red line, λ = 656 nm = 6.56 x 10^-5 cm
For the blue line, λ = 434 nm = 4.34 x 10^-5 cm
Substituting these values into the formula, we get 
θ_red = 6.56 x 10^-5 cm / (2 x 10^-4 cm/ruling) = 0.328 radians
θ_blue = 4.34 x 10^-5 cm / (2 x 10^-4 cm/ruling) = 0.217 radians
The angular separation between the two lines is the difference between these angles: 
θ = θ_red - θ_blue = 0.328 - 0.217 = 0.111 radians
Converting to degrees, we get 
θ = 0.111 x 180/π = 6.35°, which is closest to option C) 6.6°.

The Hydrogen Spectrum Has a Red Line at 656 Nm,and °\degree°

The Hydrogen Spectrum Has a Red Line at 656 Nm,and $\degree$