  We have investigated $4s\;^2S_{1/2} \rightarrow 5p\;^2P_{1/2}$ transition
($D_1$ line) of the potassium isotopes $^{39}$K, $^{40}$K, and $^{41}$K using
Doppler-free laser saturation spectroscopy. Our measurements reveal the
hyperfine splitting of the $5p\;^2P_{1/2}$ state of $^{40}$K and we have
determined the specific mass shift and the nuclear field shift constants for
the blue $D_1$ line.
