1. We determine diamagnetism using Molecular Orbital Theory.

2. A species is diamagnetic if all electrons are paired in its molecular orbitals.

3. Check each species one by one.

1. $H_2$

Total electrons $= 2$.

MO filling: $\sigma_{1s}^2$ All electrons are paired.

$\Rightarrow H_2$ is diamagnetic.

2. $He_2^+$

Total electrons $= 2+2-1=3$? Actually each He has 2 electrons, so: $2+2-1=3$ This is incorrect counting for cation; for $He_2^+$ total electrons are $2+2-1=3$ MO filling: $\sigma_{1s}^2\,\sigma_{1s}^{*1}$ One unpaired electron is present.

$\Rightarrow He_2^+$ is paramagnetic.

3. $Li_2$

Each Li has 3 electrons. Core $1s$ electrons are paired and do not affect magnetic nature; valence electrons = 2.

MO filling (valence): $\sigma_{2s}^2$ All electrons are paired.

$\Rightarrow Li_2$ is diamagnetic.

4. $Be_2$

Valence electrons $= 4$.

MO filling: $\sigma_{2s}^2\,\sigma_{2s}^{*2}$ All electrons are paired.

$\Rightarrow Be_2$ is diamagnetic.

5. $B_2$

Valence electrons $= 6$. For $B_2, C_2, N_2$ ordering is: $\sigma_{2s}<\sigma_{2s}^*<\pi_{2p_x}=\pi_{2p_y}<\sigma_{2p_z}$

Filling: $\sigma_{2s}^2\,\sigma_{2s}^{*2}\,\pi_{2p_x}^1\,\pi_{2p_y}^1$ Two unpaired electrons are present.

$\Rightarrow B_2$ is paramagnetic.

6. $C_2$

Valence electrons $= 8$.

Filling: $\sigma_{2s}^2\,\sigma_{2s}^{*2}\,\pi_{2p_x}^2\,\pi_{2p_y}^2$ All electrons are paired.

$\Rightarrow C_2$ is diamagnetic.

7. $N_2$

Valence electrons $= 10$.

Filling: $\sigma_{2s}^2\,\sigma_{2s}^{*2}\,\pi_{2p_x}^2\,\pi_{2p_y}^2\,\sigma_{2p_z}^2$ All electrons are paired.

$\Rightarrow N_2$ is diamagnetic.

8. $O_2^-$

For $O_2, F_2$ ordering is: $\sigma_{2s}<\sigma_{2s}^*<\sigma_{2p_z}<\pi_{2p_x}=\pi_{2p_y}<\pi_{2p_x}^*=\pi_{2p_y}^*$

$O_2$ has 12 valence electrons, so $O_2^-$ has 13 valence electrons.

Filling: $\sigma_{2s}^2\,\sigma_{2s}^{*2}\,\sigma_{2p_z}^2\,\pi_{2p_x}^2\,\pi_{2p_y}^2\,\pi_{2p_x}^{*2}\,\pi_{2p_y}^{*1}$ One unpaired electron is present.

$\Rightarrow O_2^-$ is paramagnetic.

9. $F_2$

Valence electrons $= 14$.

Filling: $\sigma_{2s}^2\,\sigma_{2s}^{*2}\,\sigma_{2p_z}^2\,\pi_{2p_x}^2\,\pi_{2p_y}^2\,\pi_{2p_x}^{*2}\,\pi_{2p_y}^{*2}$ All electrons are paired.

$\Rightarrow F_2$ is diamagnetic.

10. Count diamagnetic species

Diamagnetic species are: $H_2,\ Li_2,\ Be_2,\ C_2,\ N_2,\ F_2$

Total number: $6$

Hence, the number of diamagnetic species is $\boxed{6}$