calculating expectation value of angular kinetic energy

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1. The problem statement, all variables and given/known data

the origial question given is: Show that the difference in energies between 2s and 2p radial wavefunctions is equal to the energy of the angular part of the 2p wavefunction, and thus that they have the same overall energy.

hints given:a)use virial theorem to determine total k.e. b)angular part is related to L(L+1)/r²

2. Relevant equations

I know: energy = -13.6z²/n² eV

angular k.e. = (h-bar)^2/(2m_er^2)*L(L+1)*R(r)

radial k.e. = -(h-bar)^2/(2m[SUB]e[SUB])*((1/r^2)*(d/dr)*(r^2)*(dR(r)/dr))

3. The attempt at a solution

today we were told that for this problem we need to calculate <E_k> for angular and radial energy.

my question is, what is the wavefunction i use for the expectation values?

I found in my textbook the wavefunction for 2p orbital with m_l = 0 is 1/(4*sqrt(2Pi))(Z/a₀)^(5/2)(r*cos(theta)*e^Zr/2a₀). is this what im looking for


,thanks