  The paper presents the derivation of the asymptotic behavior of $\nu$-zeros
of the modified Bessel function of the imaginary order $K_{i\nu}(z)$. This
derivation is based on the quasiclassical treatment of the exponential
potential on the positive half axis. The asymptotic expression for the
$\nu$-zeros (zeros with respect to order) contains the Lambert $W$ function,
which is readily available in most computer algebra systems and numerical
software packages. The use of this function provides much higher accuracy of
the estimation comparing to known relations containing the logarithm, which is
just the leading term of $W(x)$ at large $x$. Our result ensures accuracies
sufficient for practical applications.
