Radial part of Wave Function

R[r_]  =  A r Exp[- r/2 /a0]

Normalization:

eq1  =  
      Integrate[R[r]^2 r^2,  {r,  0,  Infinity}][[2]] == 1

R1[r_]  =  R[r] /. Solve[eq1,  A][[2]]

ravg  =  
      Integrate[R1[r] r R1[r] r^2, {r, 0, Infinity}][[2]]