A metal has \(9 \times 10^{28}\) conduction electrons per \(\mathrm{m}^3\) and its resistivity is \(1 \times 10^{-8} \Omega\). m. If the drift speed of an electron in the metal is \(1.6 \times 10^6 \mathrm{~m} / \mathrm{s}\) then its mean free path is (mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\) and charge of electron \(=1.6 \times 10^{-19} \mathrm{C}\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.