Question

The number of spherical nodes in an orbital of hydrogen-like species is
A) n − l B) n − l − 1 C) n + l − 1 D) n − l − 2

Answer 1

Answer:(^_^)

Explanation:

S  

1

​  

 state spherical symmetrical means l = 0,Number of nodal points = 1 (n - l - 1) = 1

(n - 0 - 1) = 1 ∴ n = 2

Hence 2s orbital corresponds to S  

1

​  

 state

S  

2

​  

 state has only one radial node and E = ground state of H atom

E  

H  

2

⊕

​  

 

​  

 =  

1  

2

 

R

​  

(for ground state)

E in S  

1

​  

 state Li  

2+

 = -  

1  

2

 

R

​  

(but this is equal -  

n  

2

 

Z  

2

 

​  

 × R)

Since Z = 3 for Li  

2+

 ion

∴ n = 3

Since it has only one radial node:

(n - l - 1) = 1, ⇒ (3 - l - 1), ∴ l=1

Therefore, S  

2

​  

 state corresponds to 3p (n=3,l=1)

E of S  

2

​  

 state =  

n  

2

 

RZ  

2

 

​  

 = R ×  

2  

2

 

3  

2

 

​  

 =  

4

9

​  

R = 2.25 R

2.25 × E  

H  

2

⊕

​  

 

​  

 in ground state