Determine whether the radial functions for the 2s and 2p orbitals of a hydrogen atom (R2,0(r) and R2,1(r)] are eigenfunctions of the Coulombic potential energy operator: V^ = -Ze² /4πϵ₀r. If so, give the eigenvalues. If not, then calculate the expectation values of the average potential energies of an electron in 2s and 2p orbitals of a hydrogen atom. Hints: recall that the volume element in spherical polar coordinates is dv = r2sinθdrdθdΦ. Also, recall that the spherical harmonics are normalized.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

i really dont know but i will try okay.

so i think u would just add all them up and get your answer..