a$)$ The frictional coefficient, $f,$ will determine the relative mobility for two species with the same charge in the same field. Let's first assume the base unit is a simple sphere of radius $0\mathrm{.}1nm$ and the radius increases by $0\mathrm{.}1nm$ for every additional unit. $($this may not be a great approximation for a single unit, but we will get a reasonable result for longer DNA chains where the model includes the ability of the DNA chain to fold and gyrate in solution$).$ In Python, calculate the frictional coefficients for DNA molecules of $1001$ to $1010$ units long in water near $20C.$

b$)$ Now calculate, in Python, the electrophoretic mobilities in water of all single stranded DNA molecules from $1001$ to $1010$ units. How well would capillary electrophoresis in water work for this separation? Explain.