If $N_0$ is Avogadro's number, then the number of oxygen atoms in one gram equivalent of oxygen is

As we know,

Gram equivalent $=$ (mass of the atom) $/$ (equivalent weight of the atom)

Here the gram equivalent of oxygen atom is 1.

Now,

the equivalent weight of oxygen atom $=$ molar mass of oxygen atom $/n-$ factor

Equivalent weight of oxygen atom $=\frac{16}{2}=8$

So, the mass of oxygen atom = gram equivalent $\times$ equivalent weight $=1\times 8=8 g$

Number of moles $=$ weight/molar weight $=N/N_0$

$$\begin{gathered} \Rightarrow 8/16=N/N_0 \\ \Rightarrow N=N_0/2 \end{gathered}$$

Therefore, option $\left(B\right)$ is correct.