Page 181 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

172 The hydrogen atom

Table 6.1. Radial functions R nl for the hydrogen-like atom for

n ˆ 1 to 6. The variable r is given by r ˆ 2Zr=na ì
R 10 ˆ 2(Z=a ì ) 3=2 ÿr=2
e
(Z=a ì ) 3=2 ÿr=2
R 20 ˆ p  (2 ÿ r)e
2 2
(Z=a ì ) 3=2 ÿr=2
R 21 ˆ p  re
2 6

(Z=a ì ) 3=2 2 ÿr=2
R 30 ˆ p  (6 ÿ 6r ‡ r )e
9 3
(Z=a ì ) 3=2 ÿr=2
R 31 ˆ p  (4 ÿ r)r e
9 6
(Z=a ì ) 3=2 2 ÿr=2
R 32 ˆ p  r e
9 30

(Z=a ì ) 3=2 2 3 ÿr=2
R 40 ˆ (24 ÿ 36r ‡ 12r ÿ r )e
96
(Z=a ì ) 3=2 2 ÿr=2
R 41 ˆ p  (20 ÿ 10r ‡ r )r e
32 15
(Z=a ì ) 3=2
2 ÿr=2
R 42 ˆ p  (6 ÿ r)r e
96 5
(Z=a ì ) 3=2
3 ÿr=2
R 43 ˆ p  r e
96 35
(Z=a ì ) 3=2 2 3 4 ÿr=2
R 50 ˆ p  (120 ÿ 240r ‡ 120r ÿ 20r ‡ r )e
300 5
(Z=a ì ) 3=2 2 3 ÿr=2
R 51 ˆ p  (120 ÿ 90r ‡ 18r ÿ r )r e
150 30
(Z=a ì ) 3=2 2 2 ÿr=2
R 52 ˆ p  (42 ÿ 14r ‡ r )r e
150 70
(Z=a ì ) 3=2 3 ÿr=2
R 53 ˆ p  (8 ÿ r)r e
300 70
(Z=a ì ) 3=2 4 ÿr=2
R 54 ˆ p  r e
900 70

(Z=a ì ) 3=2 2 3 4 5 ÿr=2
R 60 ˆ p  (720 ÿ 1800r ‡ 1200r ÿ 300r ‡ 30r ÿ r )e
2160 6