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9 May, 07:36

Light emitted by element X passes through a diffraction grating that has 1200 slits/mm. The interference pattern is observed on a screen 75.0 cm behind the grating. First-order maxima are observed at distances of 56.2 cm, 65.9 cm, and 93.5 cm from the central maximum. What are the wavelengths of light emitted by element X?

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  1. 9 May, 07:49
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    Width of slit = 10⁻³ / 1200

    d = 8.3 x 10⁻⁷ m

    First order maxima will be observed at

    x = λD/d

    D = 75 cm = 75 x 10⁻² m

    56.2 x 10⁻² = λ₁D/d

    = λ₁ x 75 x 10⁻² / 8.3 x 10⁻⁷

    λ₁ = 56.2 x 8.3 x 10⁻⁷ / 75

    = 6.219 x 10⁻⁷ m

    = 6219 A

    Similarly

    λ₂ = 65.9 x 8.3 x 10⁻⁷ / 75

    = 7293 A

    λ₃ = 93.5 x 8.3 x 10⁻⁷ / 75

    = 10347 A
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