A line with wave number $\pu{1.028\times10^{-2} nm^{-1}}$ is emitted in the spectrum of atomic hydrogen. In what region of the electromagnetic spectrum does this line occur?

Do we find this by referring to the range of wavelength for UV, IR, etc., or is there a method for knowing which series (Lyman, Balmer, Paschen, Bracket, Pfund) this wavelength belongs to?

  • $\begingroup$ Raman spectroscopy typically uses wavenumbers, most other types of spectroscopy use the wavelength itself. Yes, knowing the wavelength you can determine if it is UV, Vis, or IR ect. Also the precision is great enough to identify the particular hydrogne line using the Rydberg formula for hydrogen. So what range? What line? $\endgroup$
    – MaxW
    Jul 4 '18 at 1:09
  • 1
    $\begingroup$ The region of the electromagnetic spectrum is all that the question is asking for. We'll give you extra credit for identifying the actual hydrogen line. $\endgroup$
    – MaxW
    Jul 4 '18 at 1:38

Wavenumbers are a unit of energy. Given that $1\mathrm{eV}$=$8100\mathrm{cm^{-1}}$, and the relations $E=h\nu$ and $c=\lambda\nu$, where $h$ is Planck’s constant, $c$ is the speed of light, and frequency $\nu$ and wavelength $\lambda$, you should be able to solve this with some simple algebra. Once you calculate the wavelength, try to find where it falls on the electromagnetic spectrum$^{[1]}$.

EM spectrum

$^{[1]}$ EM Spectrum - cyberphysics

  • $\begingroup$ True. What I'm trying to ask is that, is it possible to identify which hydrogen spectrum line it belongs to so that even without knowing the range of wavelength for UV, gamma etc. we can identify where it lies in the electromagnetic spectrum. Because we already know that lines belonging to the Lyman series are UV, Balmer series are Visible light, Paschen series are Near IR and so on. What do you think? $\endgroup$ Jul 5 '18 at 14:22
  • $\begingroup$ Sure; convert the wavelength ranges to energy ranges and see where it falls. It’s all the same. $\endgroup$
    – ringo
    Jul 5 '18 at 14:24

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