Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength

Question

Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength in the series.

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Thạch Thảo 5 years 2021-08-11T08:35:21+00:00 1 Answers 18 views 0

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  1. King
    0
    2021-08-11T08:36:23+00:00
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    Answer and Explanation:

    The computation of the shortest wavelength in the series is shown below:-

    \frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )

    Where

    \lambda represents wavelength

    R represents Rydberg’s constant

    n_f represents Final energy states

    and n_i represents initial energy states

    Now Substitute is

    1.097\times 10^7\ m^{-1}\ for\ R, \infty for\ n_i,\ 3 for\ n_i,\\\\\ \frac{1}{\lambda} = R(\frac{1}{n_f^2} - \frac{1}{n_i^2} )

    now we will put the values into the above formula

    = 1.097\times 10^7 m^{-1}(\frac{1}{3^2} - \frac{1}{\infty^2} )\\\\ = 1.097\times10^7\ m^{-1} (\frac{1}{9} )

    = 1218888.889 m^{-1}

    Now we will rewrite the answer in the term of \lambda

    \lambda = \frac{1}{1218888.889} m\\\\ = 0.82\times 10^{-6} m

    So, the whole Paschen series is in the part of the spectrum.

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