A metal surface is exposed to \(500\, \mathrm{~nm}\) radiation. The threshold frequency of the metal for photoelectric current is \(4.3 \times 10^{14}\, \mathrm{~Hz}\). The velocity of ejected electron is \(.......\,\times 10^{5} \mathrm{~ms}^{-1}\) (Nearest integer) [Use : \(\left.\mathrm{h}=6.63 \times 10^{-34}\, \mathrm{Js}, \mathrm{m}_{\mathrm{e}}=9.0 \times 10^{-31}\, \mathrm{~kg}\right]\)

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.