See my soultion and how I solved it I want to continue my solution step by step for the rest of the radial wavefunctions in Table 7.2 on the question ( for all of them) ( Provide your own work only ) :

7-3. Show that the radial functions given in Table 7.2 are normalized. TABLE 7.2 The Hydrogen-like Radial Wave Functions, Rn(r), for n = 1, 2, and 3 a Z 3/2 R10(r) = 2 e -P do Z 3/2 R20 (r) = (2- p)e-p/2 2do 3/2 R21(r ) = Z pe-P/2 V3 2do 2 Z 3/2 R30(r) = 27 (27 - 18p + 2p3)e-P/3 3do 1 3/2 R31(r) = 2Z p(6 - p)e-p/3 27 4 Z 3/2 R32 (r) = pre - p / 3 27 10 3do a. The quantity Z is the nuclear charge, and p = Zr/do, where do is the Bohr radius.7 - 3 * The radial warefunction. Racers = S ( -1- 1)1. 2 1+ 3 /2 2 n [( m + 1 )1]3 reeor / nao Lard 2r nap - . . Bohr radius , 0.5291 A 24+1 -> but : Assoriated lequerre polynomials For nornialization radial warefunction must be : OC do 12 Rit er) Rini(r) = 1 ( from The book Pg 325) * For r= 1 , LEO In ( RN, 1 2 electron density Reg (1 ) = 2 / 2 e -f , where f = Zr do [ square of the warefunction knows as the probability one It is important because it ensures that the function 15 normalizeet and the probability that particle is found somewhere in the space is equalto1] => Rio(r) = 1212 * from integral table : 3 = 4 1 xhe'dx = h! oc 1 Rio(rol " rider = 4 ( 3 ) e 2Z a o ir? dr = 41 13 2 X 2 13 x Z X for Rio (1 5)