Which one of the following species is diamagnetic in nature?

The magnetic behaviour of any molecule/ion is decided by the presence or absence of unpaired electrons in its molecular orbitals (MOs).
If every electron is paired, the species is diamagnetic; if even one electron is unpaired, it is paramagnetic.

For very light homonuclear diatomic species such as $$H_2,\,H_2^{+},\,H_2^{-},\,He_2^{+}$$ only the $$1s$$ atomic orbitals combine to give two molecular orbitals:
• the bonding orbital $$\sigma_{1s}$$ (lower energy)
• the antibonding orbital $$\sigma_{1s}^*$$ (higher energy)

Electron filling order: $$\sigma_{1s}$$ is filled first, then $$\sigma_{1s}^*$$, following Hund’s rule and Pauli principle.

Total electrons = $$2 + 1 = 3$$.
Electronic configuration: $$\sigma_{1s}^{\,2}\,\sigma_{1s}^{*\,1}$$.
One unpaired electron is present ⇒ paramagnetic.

Total electrons = $$1 + 1 = 2$$.
Electronic configuration: $$\sigma_{1s}^{\,2}$$.
All electrons are paired ⇒ diamagnetic.

Total electrons = $$2 - 1 = 1$$.
Electronic configuration: $$\sigma_{1s}^{\,1}$$.
One unpaired electron ⇒ paramagnetic.

Total electrons = $$2 + 1 = 3$$.
Electronic configuration: $$\sigma_{1s}^{\,2}\,\sigma_{1s}^{*\,1}$$.
One unpaired electron ⇒ paramagnetic.

Among the four species, only $$H_2$$ has all its electrons paired and is therefore diamagnetic.

Option B which is: H$$_2$$