Answer
$6.9\times10^{-7}N/m$
Work Step by Step
Here we use the equation $W=\frac{1}{2}Kx^{2},$ Where W-work required to compress the DNA molecule, K- spring constant, x- the compressed distance of the DNA molecule
$W=\frac{1}{2}Kx^{2}$
Let's plug known values into this equation.
$6.92\times10^{-24}J=\frac{1}{2}K\times(4.48\space nm)^{2}$
$13.84\times10^{-24}J=K\times(4.48\times10^{-9}m)^{2}$
$\frac{0.69\times10^{-24}}{10^{-18}}N/m=K$
$K=6.9\times10^{-7}\space N/m$