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Give answer of following questions.
$(i)$ Give molecular orbitals and type form by $\mathrm{LCAO}$ from $2{\rm{s}},2{{\rm{p}}_{\rm{x}}},2{{\rm{p}}_{\rm{y}}}$ and $2{{\rm{p}}_{\rm{z}}}$
$(ii)$ ${\rm{L}}{{\rm{i}}_2},{\rm{B}}{{\rm{e}}_2},{{\rm{C}}_2},{{\rm{N}}_2},{{\rm{O}}_2}{\rm{,}}{{\rm{F}}_2}$ for these molecule give energy other.
Solution
Molecular orbital formed by $LCAO$ :
| AO |
Combination of atomic $\quad$ orbitals ($LCAO$) |
Molecular orbital $(\mathrm{MO})$ |
| $2 s$ |
$\psi(2 s)+\psi(2 s)$ $\psi(2 s)-\psi(2 s)$ |
$BMO$ : $\sigma(2 s)$ $ABMO$ : $\sigma^{*}(2 s)$ |
| $2 p_{z}$ |
$\psi\left(2 p_{z}\right)+\psi\left(2 p_{z}\right)$ $\psi\left(2 p_{z}\right)-\psi\left(2 p_{z}\right)$ |
$BMO$ : $\sigma *\left(2 p_{z}\right)$ $ABMO$ : $\sigma\left(2 p_{z}\right)$ |
| $2 p_{x}$ |
$\psi\left(2 p_{x}\right)+\psi\left(2 p_{x}\right)$ $\psi\left(2 p_{x}\right)-\psi\left(2 p_{x}\right)$ |
$BMO$ : $\pi\left(2 p_{x}\right)$ $ABMO$ : $\pi *\left(2 p_{x}\right)$ |
| $2 p_{y}$ |
$\psi\left(2 p_{y}\right)+\psi\left(2 p_{y}\right)$ $\psi\left(2 p_{y}\right)-\psi\left(2 p_{y}\right)$ |
$BMO$ : $\pi\left(2 p_{y}\right)$ $ABMO$ : $\pi *\left(2 p_{y}\right)$ |
Energy order of orbitals :
– The increasing order of energy of MO for
$\mathrm{Li}_{2}, \mathrm{Be}_{2}, \mathrm{~B}_{2}, \mathrm{C}_{2}, \mathrm{~N}_{2}$ are so under
$\sigma 1 s<\sigma^{*} 1 s<\sigma 2 s<\sigma^{*} 2 s<\left[\pi 2 p_{x}=\pi 2 p_{y}\right]<\sigma 2 p_{z}<\left[\pi^{*} 2 p_{x}=\pi^{*} 2 p_{y}\right]<\sigma^{*} 2 p_{z}$
$\rightarrow$ The increasing order of energies of $\mathrm{MO}$ for $\mathrm{O}_{2}$ and $\mathrm{F}_{2}$ is given below.
$\sigma 1 s<\sigma^{*} 1 s<\sigma 2 s<\sigma^{*} 2 s<\sigma 2 p_{z}<$
${\left[\pi 2 p_{x}=\pi 2 p_{y}\right]<\left[\pi^{*} 2 p_{x}=\pi^{*} 2 p_{y}\right]<\sigma^{*} 2 p_{z}}$
