Calculate the wavelength of a nitrogen molecule moving at a speed of 523m/s.

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Calculate the wavelength of a nitrogen molecule moving at a speed of 523m/s.

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Cherry 5 years 2021-08-31T10:46:26+00:00 1 Answers 17 views 0

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  1. phucdien
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    2021-08-31T10:47:51+00:00
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    Answer:

    The de-Broglie wavelength of the nitrogen molecule is 0.0272 nm

    Explanation:

    The mass, m, of the nitrogen molecule, N₂ = 14.0076u = 28.0152 × 1.66 × 10⁻²⁷ kg

    v_{rms} of N₂ = 523 m/s

    The de-Broglie wavelength is given as follows;

    de-Broglie \, wavelength = \dfrac{h}{m\times v_{rms}}

    Where:

    h = Planck’s constant = 6.62607004 × 10⁻³⁴ m²·kg/s

    Plugging in the values, we have;

    de-Broglie \, wavelength = \dfrac{6.62607004 \times 10^{-34}}{28.0152 \times 1.66 \times 10^{-27}\times 523} = 2.72\times 10^{-11} \, m

    Hence, the de-Broglie wavelength of the nitrogen molecule = 0.0272 nm.

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