Question

Normalize the wavefunction for a 1s atomic orbital of a hydrogen-like atom with atomic number, Z: $wEKOxBnJxWfkgAAAABJRU5ErkJggg==$ , where $6ecp7H7ygQAAAABJRU5ErkJggg==$

Answer 1

If the function is normalized then, r yay dł = 1 all space since it is polar coordinate rodisiance from mucleas, has a limit 07 ora o = zenith angle, has a limit 0 = azimuth angle, has a limit 0 21. & dx = r2 sino drdo dd. 22 Pan J J y *y r2 dr. sino do dq = 1 _ 27/a. Y(,0,0) = Ne-12 Ne is a real function, 50, 4*4= N2ė - că 22 OC g2 dr. sino do dd = 1 - 2 Zr 22T 2e a 0 0 ó 21 277 A1 sin sy na przetat. Jaime do. Walf = 5 say, 224 = * = vc q x 27 dr=dx → dr = a. dx. A to let ...Ney* *e* (9) dae[co] 22 11 * ( dx = [03:26=1 , 27 51 M2 247 2A 27

> N2 93a 1 N = K ra3 -ta (0,) = + / Z317 13e NOTE: According to Gamma function, Tanpa xn-3e-4 dx = (n-1)! Cos (0)= 1 & cos = -1 Here's n = 3, so, result = 2..