Wavenumber, as used in spectroscopy and most chemistry fields, is defined as the number of wavelengths per unit distance.
The corresponding formula is
$$k=\frac{1}{\lambda}.$$
However, in theoretical physics, a wave number defined as the number of radians per unit distance and the formula is $$k=\frac{2\pi}{\lambda}.$$
Should not the definition used in physics be number of wavelengths per unit radian? If not then why?
It may vary from language to language, but in mine (French) a similar confusion exists. Both $1/\lambda$ and $2\pi/\lambda$ are called "wave number", although they aren't the same thing (the former in a frequency, the latter an angular frequency).
Although they have the same dimension (inverse length), they also have different units ($\text{m}^{-1}$ vs $\text{rad.m}^{-1}$).
It's annoying that they're called the same. However, $1/\lambda$ seems to be very rarely used outside MRI. Just difference in habits.
