(Solved): In class we looked at the electron configuration of N2 and O2 and showed that the term symbo ...

In class we looked at the electron configuration of $${\mathrm{N}}_2$$ and $${\mathrm{O}}_2$$ and showed that the term symbol for the $${\mathrm{N}}_2$$ ground state is $${}^1{?}_{\mathrm{g}}$$ and for $${\mathrm{O}}_2{}^3{?}_{\mathrm{g}},{}^1{?}_{\mathrm{g}}$$ and $${}^1{?}_{\mathrm{g}}$$ for the $$\mathrm{KK}{?}_{\mathrm{g}}{\left({\mathrm{p}}_{\mathrm{z}}\right)}^2?{\left({\mathrm{p}}_{\mathrm{z}}{\mathrm{p}}_{\mathrm{y}}\right)}^4{?}_{\mathrm{g}}^{?}{\left({\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}}\right)}^2$$ configuration. While in atoms the p-orbitals are all equivalent with $$l=1$$ and $$m_l=0\pm 1$$ in homonuclear diatomic molecules we have a bonding axis associated with $${\mathrm{p}}_z$$ and $$l=0,m_l=0$$ leading to $$?$$-bonds and $${\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}}$$ associated with $$l=1,m_l=\pm 1$$ leading to $$?$$ bonds. Hence as shown in the electron configuration above we need to separate these two bonding types. Using the tools given in class, respond to the following question: a.) The $${\mathrm{N}}_2$$ ground state configuration is $${?}_{\mathrm{u}}{\left({\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}}\right)}^4{?}_{\mathrm{g}}{\left({\mathrm{p}}_{\mathrm{z}}\right)}^2{?}_{\mathrm{g}}^{?}{\left({\mathrm{p}}_{\mathrm{x}}{\mathrm{p}}_{\mathrm{y}}\right)}^0{?}_{\mathrm{u}}^{?}{\left({\mathrm{p}}_{\mathrm{z}}\right)}^0$$. Two excited states are formed from $${?}_{\mathrm{u}}?{?}^{?}\mathrm{g}$$ and $${?}_{\mathrm{u}}?{?}_{\mathrm{g}}^{?}$$ transitions. i. Draw the MO energy level scheme for electron configurations corresponding to the ground state and the two excited states. ii. Obtain the term symbols for the two excited states and order them according to Hund's rules. iii. Write the wave function for the lowest energy terms of the two excited states, $${?}_{\text{TOT }}={?}_{\text{space }}{?}_{\text{sspin }}$$