The following data represent force ( $f$, in picoNewtons) versus extension ( $h$, in microns) for a single $\lambda$-DNA molecule, measured at room temperature in salt solutions (S.B. Smith, L. Finzi, and C. Bustamante, Science, 258, 1122, 1992). These data therefore represent an opportunity to test basic assumptions of the theory of rubber elasticity. Try to fit these data in three ways. First, use the Gaussian expression; restrict the fit to the low extension part of the curve. Second, try the inverse Langevin function, approximated in Equation 10.6.4. Third, try the following formula derived for the worm-like chain (C. Bustamante, J. Marko, E. Siggia, and S. Smith, Science, 265, 1599, 1994; recall Chapter 6).
(Table cant copy)
$$
f=\frac{k T}{\ell_{\mathrm{p}}}\left(\frac{1}{4(1-h / L)^2}-\frac{1}{4}+\frac{h}{L}\right)
$$
Comment on the success or failure of the various expressions and provide values for the contour length, $L$, and the persistence length.