I assume you're asking how to generate a bar plot with your given function, and not how to solve some sort of thing.
This can easily be done with BarLegend
F[x_] := Sqrt[(5*10^-6)*x^2*(5*10^-9)^y] /. y -> Sqrt[Tan[x]]
Plot[F[x], {x, 0, 1}, ColorFunction -> "Rainbow",PlotLegends -> BarLegend["Rainbow"]]
Plot[Sqrt[x], {x, 0, 1}, ColorFunction -> "Rainbow", PlotLegends -> BarLegend["Rainbow"]]