= Solution
The weak-<force> <spring constant> is
$$
\boxed{k_{\rm chain}=\frac{3k_BT}{Nb^2}.}
$$
Using the literal printed $N=186$, $b=7\,\mathrm{nm}$ at $25^\circ\mathrm C=298.15\,\mathrm K$ gives
$$
\boxed{k_{\rm literal}=1.355\times10^{-6}\,\mathrm{N\,m^{-1}}=1.355\,\mathrm{pN\,\mu m^{-1}}.}
$$
This is a calculation with the quoted parameters, not a self-consistent fit to the plotted $26\,\mu\mathrm m$ contour. If instead $N=186$ and $L_c=26\,\mu\mathrm m$ are retained, then $b=L_c/N$ and $k=3.40\times10^{-9}\,\mathrm{N\,m^{-1}}$. Retaining $b=7\,\mathrm{nm}$ and $L_c=26\,\mu\mathrm m$ gives $k=6.79\times10^{-8}\,\mathrm{N\,m^{-1}}$. These distinct alternatives quantify the unresolved parameter inconsistency rather than silently choosing a correction.
The restoring <force> is entropic. Stretching selects a small fraction of the many disordered orientations, reducing <conformational entropy>. The <Gaussian chain> <free energy>[free-energy] cost is $\Delta\mathcal F\simeq3k_BTR^2/(2Nb^2)$, whose <gradient> gives the Hooke-law coefficient above. In an ideal inextensible chain, individual bonds need not change their length to generate this <force>.
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