In an experiment you measure a first-order red line for Hydrogen at an angle difference of ΔΘ = 22.78o. The diffraction grating you are usin

Question

In an experiment you measure a first-order red line for Hydrogen at an angle difference of ΔΘ = 22.78o. The diffraction grating you are using has 5900 lines per cm.

a) What is the wavelength of this light?

b) What is the value of Rydberg’s constant for this measurement?

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Vân Khánh 4 years 2021-08-06T01:18:48+00:00 1 Answers 19 views 0

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  1. thugiang
    0
    2021-08-06T01:20:25+00:00
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    Answer:

    a) wavelength = 656.3 nm

    b)  the value of Rydberg’s constant for this measurement is 1.097 × 10⁷ m⁻¹

    Explanation:

    Given that;

    angle of diffraction Θₓ = 22.78°

    incident angle Θ₁ = 0

    slit separation d  = 5900 lines per cm = 1/5900 cm = 10⁻²/5900 m = 0.01/5900 m

    order of diffraction n = 1

    wavelength λ = ?

    to find the wavelength, we use the expression

    λ = d (sinΘ₁ + sinΘₓ) / n

    To find the wavelength λ;

    λ = 0.01/5900 × (sin0 + sin22.78° )

    λ = 6.5626 × 10⁻⁷ m

    λ = 656.3 x 10⁻⁹ m

    ∴ λ = 656.3 nm

    b)

    According Balnur’s  series spectral lines; n₁ = 3, n₂ = 2 and

    λ = R [ 1/n₂² – 1/n₁²]

    where  R is Rydberg’s constant

    from λ = R [ 1/n₂² – 1/n₁²]

    R = 1/λ [n₂²n₁² / n₁² – n₂²]

    R = 10⁹/ 656.3 [ 9 × 4 / 9 – 4 ]

    R = 1.097 × 10⁷ m⁻¹

    Therefore the value of Rydberg’s constant for this measurement is 1.097 × 10⁷ m⁻¹

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