Introduction:
The stability of molecules is determined by their bonding nature. MO theory is one of the popular theories that explain the stability of molecules. In this theory, the stability of molecules is determined by the energy of the molecular orbitals. In this context, we will discuss the stability of b2 and f2 molecules.

Bonding in b2 and f2:
Both b2 and f2 molecules have a total of 14 electrons. In b2, the two electrons occupy the sigma bonding orbital, two electrons occupy the sigma anti-bonding orbital, and ten electrons occupy the pi bonding orbitals. In f2, the two electrons occupy the sigma bonding orbital, two electrons occupy the sigma anti-bonding orbital, and ten electrons occupy the pi bonding orbitals.

Energy Level Diagram:
The energy level diagram of b2 and f2 shows that the energy required to break the pi bonding orbitals of b2 is less than the energy required to break the pi bonding orbitals of f2. Therefore, b2 is more stable than f2.

Explanation:
In b2, the pi bonding orbitals are stabilized by the interaction of the two half-filled atomic orbitals of boron atoms. The pi bonding orbitals are lower in energy than the sigma anti-bonding orbitals. Hence, the energy required to break the pi bonding orbitals of b2 is less than the energy required to break the pi bonding orbitals of f2.

In f2, the pi bonding orbitals are destabilized by the interaction of the two half-filled atomic orbitals of fluorine atoms. The pi bonding orbitals are higher in energy than the sigma anti-bonding orbitals. Hence, the energy required to break the pi bonding orbitals of f2 is more than the energy required to break the pi bonding orbitals of b2.

Conclusion:
Based on the energy level diagram of molecular orbitals, it can be concluded that b2 is more stable than f2. The energy required to break the pi bonding orbitals of b2 is less than the energy required to break the pi bonding orbitals of f2.

Both b2 and f2 have same bond order which is a responsible factor for stability but stability also depends upon bond energy of the molecule
b2 bond has bond energy = 280 KJ/mol
while f2 bond has bond energy = 155KJ/mol
hence the more the bond energy the more is the stability of the molecule.
so, b2 is more stable.