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Are we justified in using a nonrelativistic treatment for the speed of an electron in the hydrogen atom?

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Find the average distance between the electron and proton in the Hydrogen ground-state. Use: <r> = ∫dr r*P(r) [bounds from 0 to +infinity: sorry I don't know how to properly type integrals] where ϕ(r) = Ae-r/aB is the ground-state solution of the radial Schrodinger equation for the Hydrogen atom (aB is Bohr's radius), and P(r) = 4πr2|ϕ(r)|2is the probability density that the electron would be located in the spherical shell between r and r + dr. First normalize the wavefunction to obtain the constant A: ∫dr P(r) = 1 [bounds from 0 to +infinity again]
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Compute and compare the electrostatic and gravitational forces in the classical hydrogen atom, assuming a radius 5.3 x 10-11 m.
Calculate the ionization energy of helium using the variational principle. The ionization energy is the difference between the ground state of neutral He (with two electrons), and the ground state of He* (with one electron removed). The ground state of neutral He we will calculate in class to be approximately -75 eV using the variational method.