  We present a unified scaling description for the dynamics of monomers of a
semiflexible chain under good solvent condition in the free draining limit. We
consider both the cases where the contour length $L$ is comparable to the
persistence length $\ell_p$ and the case $L\gg \ell_p$. Our theory captures the
early time monomer dynamics of a stiff chain characterized by $t^{3/4}$
dependence for the mean square displacement(MSD) of the monomers, but predicts
a first crossover to the Rouse regime of $t^{2\nu/{1+2\nu}}$ for $\tau_1 \sim
\ell_p^3$, and a second crossover to the purely diffusive dynamics for the
entire chain at $\tau_2 \sim L^{5/2}$. We confirm the predictions of this
scaling description by studying monomer dynamics of dilute solution of
semi-flexible chains under good solvent conditions obtained from our Brownian
dynamics (BD) simulation studies for a large choice of chain lengths with
number of monomers per chain N = 16 - 2048 and persistence length $\ell_p = 1 -
500$ Lennard-Jones (LJ) units. These BD simulation results further confirm the
absence of Gaussian regime for a 2d swollen chain from the slope of the plot of
$\langle R_N^2 \rangle/2L \ell_p \sim L/\ell_p$ which around $L/\ell_p \sim 1$
changes suddenly from $\left(L/\ell_p \right) \rightarrow \left(L/\ell_p
\right)^{0.5} $, also manifested in the power law decay for the bond
autocorrelation function disproving the validity of the WLC in 2d. We further
observe that the normalized transverse fluctuations of the semiflexible chains
for different stiffness $\sqrt{\langle l_{\bot}^2\rangle}/L$ as a function of
renormalized contour length $L/\ell_p$ collapse on the same master plot and
exhibits power law scaling $\sqrt{\langle l_{\bot}^2\rangle}/L \sim
(L/\ell_p)^\eta $ at extreme limits, where $\eta = 0.5$ for extremely stiff
chains ($L/\ell_p \gg 1$), and $\eta = -0.25$ for fully flexible chains.
