Question

One of the excited states of a C2 molecule has the electron configuration: (?1s)2(?1s*)2(?2s)2(?2s*)1(? 2p)4(?2p)1.

Answer 1

Concepts and reason

The bond order is the number of bonds present between two atoms. This is calculated using molecular orbital theory.

Higher the value of bond order lesser will be the bond length.

Fundamentals

Molecular orbital theory is used to explain bonding in molecules using linear combination of atomic orbitals. According to molecular orbital theory, the atomic orbitals combine linearly to form molecular orbitals. The number of atomic orbitals combining is equal to the number of molecular orbitals formed. These molecular orbitals are further divided into two parts bonding and anti-bonding molecular orbitals (represented using “*” at superscript).

The molecular orbital diagrams for ${{\rm{C}}_2}$ in excited state is as follows:

The bond order can be calculated for these molecules using the following formula:

${\rm{Bond order}} = \frac{1}{2}\left( {{\rm{No}}{\rm{. of bonding electrons}} - {\rm{No}}{\rm{. of Antibonding electrons}}} \right)$

For ${{\rm{C}}_2}$ in excited state,

${{\rm{C}}_2}$ in excited state have 9 bonding electrons and 3 anti-bonding electrons. Therefore, its bond order will be:

$\begin{array}{c}\\{\rm{Bond order}} = \frac{1}{2}\left( {9 - 3} \right)\\\\ = 3\\\end{array}$

The bond order can be calculated for these molecules using the following formula:

${\rm{Bond order}} = \frac{1}{2}\left( {{\rm{No}}{\rm{. of bonding electrons}} - {\rm{No}}{\rm{. of Antibonding electrons}}} \right)$

For ${{\rm{C}}_2}$ in ground state,

${{\rm{C}}_2}$ in excited state have 8 bonding electrons and 4 anti-bonding electrons. Therefore, its bond order will be:

$\begin{array}{c}\\{\rm{Bond order}} = \frac{1}{2}\left( {8 - 4} \right)\\\\ = 2\\\end{array}$

The bond order of excited state and ground state are in order as given below:

${\rm{C}}_2^{}\left( {{\rm{ground}}\;{\rm{state}}} \right) < {\rm{C}}_2^{}\left( {{\rm{excited}}\;{\rm{state}}} \right)$

Ans:

The bond order of ${{\rm{C}}_2}$ in excited state is 3.

The bond order of ${{\rm{C}}_2}$ in ground state is 2.

The bond length of excited state in comparison to the ground state is

Bond length (excited state) Bond length (ground state)