c.Solution of R equation 1 dR(r) 8πme(E+ e R(r)dr Or 3 )r2=B 4π6J Solution R(r)=N·ep2L2H n+1(p) 2Z p=2ar= 4πEh2 nao ao =0.529 me2 ao is called Bohr radius n--1 2(p)=-I) {n+10}2 k=0 (n-1-1-k)(21+1+k)Ik necessary condition:n /+1 hence,n 1,2,3,...... n: Principal quantum number 1=0,1,2 Zh2 E= 8元2na 8π2ma R is called Rydberg constant with the value of 13.6 eV Example: 3/2 n=1,=0 R0=2 e-pl2 do n=2,1=0 3/2 1 Z R20 (2-p)ep/2 2W2 aoc. Solution of R equation β πε π + + = ∂ ∂ 2 0 2 2 2 2 ) 4 ( 8 ) ( ) ( ( ) 1 r r ze E h m r dR r r R r dr e Solution /2 2 1 () ( ) l Rr N e Ln l ρ ρ − + = ⋅ + 0 2 2 Z r r na ρ α = = 1 2 21 1 0 {( )!} ( ) ( 1) ( 1 )!(2 1 )! ! n l lk k m l k n l L nl k l kk ρ ρ − − + + + = + = − −−− ++ ∑ a0 is called Bohr radius o 2 2 0 0 0.529 A 4 = = m e a e πε h necessary condition: n ≥ l+1 hence, n = 1, 2, 3,…… l = 0, 1, 2, …… n: Principal quantum number 22 2 2 2 2 22 2 2 2 2 0 0 ( ) 8 8 Z h hZ Z E R π π mn a ma n n =− =− ⋅ =− R is called Rydberg constant with the value of 13.6 eV n=1, l=0 Example: 3/2 / 2 10 0 2 Z R e a −ρ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ n=2, l=0 / 2 3/ 2 0 20 (2 ) 2 2 1 ρ ρ − − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = e a Z R