53. The radial probability function for the ground state of hydrogen is P (r) =(4r2/a3)e-2r/a, where a is
" the Bohr radius. (See Eq. 40-31.) We want to evaluate the integral P (r) dr. Eq. 15 in the integral 0 table of Appendix E is an integral of this form. We set n = 2 and replace a in the given formula with 2/a and x with r. Then
" " 4 4 2 P (r) dr = r2e-2r/a dr = =1 . a3 a3 (2/a)3 0 0