Question

4. Consider the hypothetical linear Hs ion. (a) Draw the crude shapes of the molecular orbitals for the linear H5 ion. Pay particular attention to locating the nodes. Identfy the orbitals as g or u as appropriate. (b) Draw a molecular orbital diagram for the linear Hs ion and fill it in with electrons (c) Is the linear Hs ion expected to be stable? Why or why not (d) How many bands are predicted in the photoelectron spectrum of the linear Hs molecule.

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Answer 1

nth orbital will have n-1 nodes.

Thus orbitals : 1σ_g, 1σ_u, 2σ_g, 2σ_u, and 3σ_g will have : 0,1,2,3,4 nodes respectively.

Energy order : 1σ_g< 1σ_u (bonding MOs) <2σ_g (Nonbonding MOs) < 2σ_u < 3σ_g (Antibonding MOs)

Electrons shall be filled as hund's rule with increasing energy : 1σ_g²1σ_u²

Thus both bonding orbitals are occupied , no electron in antibonding orbitals : thus it can be expected to be stable.

2209 Anh 936g I Bonding L 26 26u Nodes - 2 Narbonding 269 00101010 ooooo Nodes 130 00000 Nodes: 2 00000 Nodes 11 00000 Noses: 0 1969 Inde y love Bonding 169 linear Hit Mo (1682 166 ) [H-H-HH-H] 1 linear

(d)

A photoelecton spectrum show the relative energies of occupied molecular orbitals by ionization. (i.e. ejection of an electron).

Linear H₅ molecule :

Electrons shall be filled as hund's rule with increasing energy : 1σ_g²1σ_u² 2σ_g¹

Since three MO orbitals (different) energy are occupied , thus we can expect 3 bands in photoelectron spectroscopy.