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.

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.

$\sigma 1 s<\sigma^{*} 1 s<\sigma 2 s<\sigma^{*} 2 s<\sigma 2 p_{z}<$

${\left[\pi 2 p_{x}=\pi 2 p_{y}\right]<\left[\pi^{*} 2 p_{x}=\pi^{*} 2 p_{y}\right]<\sigma^{*} 2 p_{z}}$