= Solution
Under an additional thermalization assumption, an opaque <star> emits approximately <black-body radiation> characterized by the <temperature> near the layer from which thermal <photons> escape. <Planck's law> gives a <Rayleigh-Jeans law> low-<frequency> tail $B_\nu\propto T\nu^2$ and a <Wien approximation> high-<frequency> tail $B_\nu\propto\nu^3e^{-h\nu/(k_BT)}$.
Using the gas-dominated <temperature> profile in <2/d> and the local escape criterion in <2/c>, the model's putative emission <temperature> for the <Sun>'s parameters would be
$$
T_{\rm esc}\simeq T_c\frac{\Delta R_{\rm esc}}R
\simeq16.1\,\mathrm K.
$$
Using radial $\tau=1$ instead gives $22.8\,\mathrm K$. The <frequency form of Wien's displacement law> for the maximum of $B_\nu$ is $h\nu_{\max}/(k_BT)=2.82144$, so these two prescriptions predict
$$
\boxed{\nu_{\max}\simeq9.5\times10^{11}\,\mathrm{Hz}
\quad\hbox{or}\quad1.34\times10^{12}\,\mathrm{Hz},}
$$
respectively, in the far infrared/submillimetre region. These are conditional estimates for this model, not observed solar peaks. A realistic solar <effective temperature> near $5.8\times10^3\,\mathrm K$ gives $\nu_{\max}\simeq3.4\times10^{14}\,\mathrm{Hz}$ in $B_\nu$. The maximum of $B_\lambda$ occurs near $0.50\,\mathrm{\mu m}$; it is not obtained by simply taking $c/\nu_{\max}$, because spectral densities transform with a <Jacobian determinant>.
The model is unsuitable for the solar <photosphere>: fully ionized <hydrogen> at $16$–$23\,\mathrm K$ is inconsistent with thermal ionization, and the assumed opacity and near-surface <temperature> gradient do not resemble the <Sun>'s. Even its central <temperature> is substantially below the actual solar value, about $1.6\times10^7\,\mathrm K$.
There is a further logical limitation: the question retains \b[only <Thomson scattering>]. In its coherent, cold-<electron> limit, this redistributes <photon> directions without generating a <Planck photon distribution>. For a concrete counterexample, monochromatic injected radiation remains monochromatic after any number of such elastic scatterings; large <optical depth> cannot turn it into <black-body radiation>. True absorption and emission, or a specified pre-existing thermal radiation field with appropriate energy exchange, are missing. Thus an approximately <blackbody> emergent spectrum is the usual additional physical assumption, while the stated scattering-only model does not uniquely predict an emergent spectrum or its peak.
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