= Spectroscopic wavenumber
{title2=$\tilde\nu=1/\lambda_0$}
A <spectroscopic wavenumber> commonly means the reciprocal of the vacuum <wavelength> $\lambda_0$ of <electromagnetic radiation>, often in $\mathrm{cm^{-1}}$. It is an ordinary <spatial frequency>, so the vacuum angular <wavenumber> is $K_0=2\pi\tilde\nu$. Specify vacuum or in-medium <wavelength>: the same <frequency> can have different <wavelengths> in different media. IUPAC's “wavenumber in medium” entry defines the in-medium reciprocal $1/\lambda$ and notes that unqualified spectroscopic usage often means the vacuum reciprocal.<wavenumber in medium>{ref}
For example, a vacuum <wavelength> of $500\,\mathrm{nm}=5\times10^{-5}\,\mathrm{cm}$ corresponds to $\tilde\nu=20000\,\mathrm{cm^{-1}}=2\times10^6\,\mathrm{m^{-1}}$. Multiplication by $2\pi$ gives $K_0=4\pi\times10^6\,\mathrm{rad\,m^{-1}}$. Converting centimetres to metres and converting cycles to <radians> are separate operations.
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