Chapter 12, Problem 12.60E

Interpretation Introduction

Interpretation:

The molecular electronic configurations for all diatomic molecules shown in Figure 12.23 are to be predicted.

Concept introduction:

Electronic configuration tells about the arrangement of the electrons in each subshell of an atom. The distribution of the electrons in the molecules is described by the molecular orbital theory.

Answer to Problem 12.60E

The molecular electronic configurations for molecules ${\text{Li}}_2$, ${\text{Be}}_2$, ${\text{B}}_{\text{2}}$, ${\text{C}}_{\text{2}}$, ${\text{N}}_{\text{2}}$, ${\text{O}}_{\text{2}}$, ${\text{F}}_{\text{2}}$ and ${\text{Ne}}_{\text{2}}$ are ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^1,{\pi }_{\mu }2p_y^1\right)$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right){\left({\sigma }_{g}2p_z\right)}^2$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^1,{\pi }_g^{*}2p_y^1\right)$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^2,{\pi }_g^{*}2p_y^2\right)$ and ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^2,{\pi }_g^{*}2p_y^2\right){\left({\sigma }_{\mu }^{*}2p_z\right)}^2$ respectively.

Explanation of Solution

The diatomic molecules shown in Figure 12.23 are ${\text{Li}}_2$, ${\text{Be}}_2$, ${\text{B}}_{\text{2}}$, ${\text{C}}_{\text{2}}$, ${\text{N}}_{\text{2}}$, ${\text{O}}_{\text{2}}$, ${\text{F}}_{\text{2}}$ and ${\text{Ne}}_{\text{2}}$.

The number of electrons in ${\text{Li}}_2$ is $6$. Thus, the molecular electronic configurations for ${\text{Li}}_2$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2$.

The number of electrons in ${\text{Be}}_2$ is $8$. Thus, the molecular electronic configurations for ${\text{Be}}_2$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2$.

The number of electrons in ${\text{B}}_{\text{2}}$ is $10$. Thus, the molecular electronic configurations for ${\text{B}}_{\text{2}}$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^1,{\pi }_{\mu }2p_y^1\right)$.

The number of electrons in ${\text{C}}_{\text{2}}$ is $12$. Thus, the molecular electronic configurations for ${\text{C}}_{\text{2}}$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)$.

The number of electrons in ${\text{N}}_{\text{2}}$ is $14$. Thus, the molecular electronic configurations for ${\text{N}}_{\text{2}}$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right){\left({\sigma }_{g}2p_z\right)}^2$.

The number of electrons in ${\text{O}}_{\text{2}}$ is $16$. Thus, the molecular electronic configurations for ${\text{O}}_{\text{2}}$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^1,{\pi }_g^{*}2p_y^1\right)$.

The number of electrons in ${\text{F}}_{\text{2}}$ is $18$. Thus, the molecular electronic configurations for ${\text{F}}_{\text{2}}$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^2,{\pi }_g^{*}2p_y^2\right)$.

The number of electrons in ${\text{Ne}}_{\text{2}}$ is $18$. Thus, the molecular electronic configurations for ${\text{Ne}}_{\text{2}}$ is ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^2,{\pi }_g^{*}2p_y^2\right){\left({\sigma }_{\mu }^{*}2p_z\right)}^2$.

Conclusion

The molecular electronic configurations for molecules ${\text{Li}}_2$, ${\text{Be}}_2$, ${\text{B}}_{\text{2}}$, ${\text{C}}_{\text{2}}$, ${\text{N}}_{\text{2}}$, ${\text{O}}_{\text{2}}$, ${\text{F}}_{\text{2}}$ and ${\text{Ne}}_{\text{2}}$ are ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^1,{\pi }_{\mu }2p_y^1\right)$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right){\left({\sigma }_{g}2p_z\right)}^2$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^1,{\pi }_g^{*}2p_y^1\right)$, ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^2,{\pi }_g^{*}2p_y^2\right)$ and ${\left({\sigma }_{g}1s\right)}^2{\left({\sigma }_g^{*}1s\right)}^2{\left({\sigma }_{g}2s\right)}^2{\left({\sigma }_g^{*}2s\right)}^2{\left({\sigma }_{g}2p_z\right)}^2\left({\pi }_{\mu }2p_x^2,{\pi }_{\mu }2p_y^2\right)\left({\pi }_g^{*}2p_x^2,{\pi }_g^{*}2p_y^2\right){\left({\sigma }_{\mu }^{*}2p_z\right)}^2$ respectively.