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16 July, 00:08

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. n = 4 → n = 3b. n = 5 → n = 4c. n = 5 → n = 3

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  1. 16 July, 00:34
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    a. 1875 nm

    b. 4051 nm

    c. 1282 nm

    These all are infrared electromagnetic radiation.

    Explanation:

    Our strategy here is to utilize the Rydberg equation for hydrogen atom electronic transition.

    1/λ = Rh x (1/n₁² - 1/n₂²) where λ is the wavelength

    Rh is Rydberg constant

    n₁ and n ₂ are the energy levels (n₁ < n₂)

    Now lets star the calculations.

    a. n₁ = 3, n₂ = 4

    1/λ = 1.097 x 10⁷ / m x (1/3² - 1/4²) = 5.333 x 10⁵/m

    λ = 1 / (5.333 x 10⁵ / m) = 1.875 x 10⁻⁶ m

    Converting λ to nanometers:

    1.875 x 10⁻⁶ m x (1 x10⁹ nm/m) = 1875 nm

    b. n₁ = 4, n₂ = 5

    1/λ = 1.097 x 10⁷ / m x (1/4² - 1/5²) = 2.468 x 10⁵/m

    λ = 1 / (2.468 x 10⁵/m) = 4.051 x 10⁻⁶ m

    4.051 x 10⁻⁶ m x (1 x10⁹ nm/m) = 4051 nm

    c. n₁ = 3, n₂ = 5

    1/λ = 1.097 x 10⁷ / m x (1/3² - 1/5²) = 7801 x 10⁵/m

    λ = 1 / (7801 x 10⁵/m) = 1282 x 10⁻⁶ m

    1282 x 10⁻⁶ m x (1 x10⁹ nm/m) = 1282 nm

    All of these transitions fall in the infrared region of the spectrum.
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