Answer
See answers.
Work Step by Step
Calculate the angles for the first-order diffraction line using equation 24–2a.
$$dsin\theta=m\lambda$$
$$\theta=sin^{-1}\frac{m\lambda}{d}$$
For first order, m = 1, and we also use the fact that the reciprocal of the slit separation d (in meters) is the number of lines per meter. Find the angles for each of the elements, using the appropriate red wavelength.
$$\theta_{H}=sin^{-1}((1)(6.56\times10^{-7}m)(3.60\times10^5/m))=13.7^{\circ}$$
$$\theta_{Ne}=sin^{-1}((1)(6.50\times10^{-7}m)(3.60\times10^5/m))=13.5^{\circ}$$
$$\theta_{Ar}=sin^{-1}((1)(6.97\times10^{-7}m)(3.60\times10^5/m))=14.5^{\circ}$$