The Hückel molecular orbital of benzene that is degenerate with the molecular orbital \(\frac{1}{2}\)(χ2 + χ3 − χ5 − χ6), is

Explanation:-

• For, the Hückel molecular orbital 

​\(\frac{1}{2}\)(χ2 + χ3 − χ5 − χ6), the number of nodes is 2,

• Thus, the degenerate molecular orbital with this molecular orbital must also have 2 nodes.

(1) For the molecular orbital \(\frac{1}{\sqrt{12}}\)(2χ1 + χ2 − χ3 − 2χ4 − χ5 + χ6)

The number of nodes is = 2

(2) For the molecular orbital \(\frac{1}{2}\)(χ2 − χ3 + χ5 − χ6)

The number of nodes = 3

(3) For the molecular orbital \(\frac{1}{\sqrt{12}}\)(2χ1 − χ2 − χ3 + 2χ4 − χ5 − χ6)

The number of nodes = 3

(3) For the molecular orbital \(\frac{1}{\sqrt{6}}\)(χ1 − χ2 + χ3 − χ4 + χ5 − χ6)

The number of nodes = 5

• Thus, the Hückel molecular orbital of benzene ​\(\frac{1}{\sqrt{12}}\)​(2χ1 + χ2 − χ3 − 2χ4 − χ5 + χ6) also has 2 nodes.

Conclusion:-

Hence, the Hückel molecular orbital of benzene that is degenerate with the molecular orbital \(\frac{1}{2}\)​(χ2 + χ3 − χ5 − χ6), is​ \(\frac{1}{\sqrt{12}}\)(2χ1 + χ2 − χ3 − 2χ4 − χ5 + χ6)