= Solution
For a three-dimensional <worm-like chain>, the tangent correlation length is $l_p=B/(k_BT)$, where $B$ is the <filament bending modulus>. The measured <persistence length> therefore gives
$$
\boxed{B=k_BT l_p=(4.14\times10^{-21})(2.0\times10^{-8})=8.28\times10^{-29}\,\mathrm{N\,m^2}.}
$$
Represent the <actin> filament as an isotropic solid circular cylinder with diameter $d=10^{-9}\,\mathrm m$. Its <second moment of area> is $I=\pi d^4/64=4.909\times10^{-38}\,\mathrm{m^4}$. Since $B=EI$,
$$
\boxed{E=\frac{64k_BT l_p}{\pi d^4}=1.69\times10^9\,\mathrm{Pa}.}
$$
This is an effective <Young's modulus> within the given continuum cross-sectional model; the numerical diameter and persistence length must not be replaced by unrelated typical biological values.
The same measurement corrects the independent-link approximation: the <Kuhn length> is $b_K=2l_p=40\,\mathrm{nm}$, with $N_K=L/b_K=2.5\times10^9$. Thus the long-chain entropic stiffness is $3k_BT/(2l_pL)=3.105\times10^{-15}\,\mathrm{N\,m^{-1}}$, and the root-mean-square end-to-end distance is $2\,\mathrm{mm}$. For comparison, the material axial stiffness is $EA/L=1.325\times10^{-11}\,\mathrm{N\,m^{-1}}$, using $A=\pi d^2/4$. The corrected coil response remains much softer than axial backbone stretching.
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