Respuesta :
Answer:
Excited state bond order = 3
Ground state bond order = 2
Bond length excited state < bond length ground state
Explanation:
a) Bond order in excited state:
The given excited state configuration for C2 is:
(σ1s)²(σ1s*)²(σ2s)²(σ2s*)¹(π 2p)⁴(σ2p)¹
Here '*' denote antibonding orbitals
The number of electrons in bonding orbitals are 9
Number of electrons in antibonding orbitals are 3
[tex]Bond\ order = \frac{1}{2} [Bonding\ electrons- Antibonding\ electrons]\\\\Bond\ order = \frac{1}{2} [9-3] = 3[/tex]
b) Bond order in ground state
The ground state configuration for C2 is:
(σ1s)²(σ1s*)²(σ2s)²(σ2s*)²(π 2p)⁴
Here '*' denote antibonding orbitals
The number of electrons in bonding orbitals are 8
Number of electrons in antibonding orbitals are 4
[tex]Bond\ order = \frac{1}{2} [Bonding\ electrons- Antibonding\ electrons]\\\\Bond\ order = \frac{1}{2} [8-4] = 2[/tex]
c) Comparison of bond length
Bond length is inversely proportional to the bond order.
Higher the bond order lower is the bond strength and vice versa
For C2:
The ground state bond order = 2
Excited state bond order = 3
Therefore, bond length in the excited state is smaller than that in the ground state
The bond order of the excited state is 3 and the bond length will be shorter than the bond length in the ground state.
The excited state is a higher energy state of a molecule. A molecule enters an excited state after absorbing energy. C2 has a ground state molecular orbital configuration of; σ1s2 σ*1s2 σ2s2 σ*2s 2 π2p4.
When in excited state, one electron is promoted to higher energy σ2p orbital and the electron configuration now is; (σ1s)2(σ1s*)2(σ2s)2(σ2s*)1(π 2p)4(σ2p)1.
The bond order of this excited state is obtained from; Number of bonding electrons - Number of antibonding electrons/2
Hence, bond order = 9 - 3/2 = 6/2 = 3.
A bond order of three means that the bond is a triple bond. The higher the bond order, the shorter the bond length. Hence, the bond length of this excited state will be shorter compared to that of the ground state of C2 where the bond order is 2.
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