. The yellow light from a helium discharge tube has a wavelength of 587.5 nm. When this light illuminates a certain diffraction grating it p

Question

. The yellow light from a helium discharge tube has a wavelength of 587.5 nm. When this light illuminates a certain diffraction grating it produces a second-order principal maximum at an angle of 1.170°. Calculate the number of lines per centimeter on the grating.

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Thiên Hương 4 years 2021-07-19T07:12:23+00:00 1 Answers 46 views 0

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  1. Edana
    0
    2021-07-19T07:13:51+00:00
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    Answer: 344.8 lines/cm

    Explanation:

    Given

    Wavelength of the light, λ = 587.5 nm

    Angle, θ = 1.17°

    To solve, we use the formula

    Wsin θ = mλ, where m is first order, so m = 1

    Converting the nm to cm, we have 587.5*10^9 * 100 = 587.5 * 10^-7 cm

    So, taking mλ/sin θ = W

    (1)(587.5*10^-7 cm) / sin1.17° = W

    W = 587.5*10^-7 cm / 0.020

    W = 0.0029

    But since it has to be in lines/cm, so take the inverse:

    1 / 0.0029 cm

    = 344.8 lines/cm

    Therefore, the lines/cm on the grating is 344.8 lines/cm

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