Step 1: Use the mass ratio:
28 g of $\text{N}_2$ is exactly one mole, which holds $6.022\times10^{23}$ molecules. So the molecule count is directly proportional to the mass taken.
Step 2: Scale up to 70 g:
Mass ratio: $70/28 = 2.5$.
Molecules $= 2.5 \times 6.022\times10^{23}$.
Since $2.5\times 6.022 = 15.055$, we get $15.055\times10^{23} = 1.5055\times10^{24}$ molecules.
Step 3: Compare with the options:
Only option (A) has the digits 1.5055 with the power $10^{24}$. Option (C), $3.011\times10^{24}$, is 5 mol, so it belongs to 140 g. Options (B) and (D) are a factor of ten smaller and belong to 7 g and 14 g.
Final Answer:
The sample is 2.5 times one mole of $\text{N}_2$, so it has $1.5055\times10^{24}$ molecules, option (A).
\[ \boxed{1.5055\times 10^{24}\text{ (A)}} \]