A $Na$ atom emits a photon of wavelength $590\ nm$ and recoils with velocity $v$, find $v$?

The solution provided is as :

$v=\dfrac{h}{m\lambda}=\dfrac{6.626\times 10^{-34}}{(23\times 1.67\times 10^{-27})\cdot (590\times 10^{-9})}$.

Now my doubt is that according to De Broglie hypothesis a particle of mass $m$ moving with speed $v$ behaves in some ways like waves of wavelength $\lambda$, but how the author can use $\lambda$ given in problem as it is of the photon not of $Na$