  Underground argon (UAr) with lower cosmogenic activities of $^{39}Ar$ and
$^{42}Ar$ has been planned as a detector in detecting scintillation light and
charge collection using time projection chambers for dark matter searches and
as a veto detector in suppressing backgrounds for neutrinoless double beta
decay (0$\nu\beta\beta$) experiments. Long-lived radioactive isotopes,
$^{39}Ar$ and $^{42}Ar$, can also be produced on the surface when UAr is pumped
out from a deep well. Understanding the production of long-lived isotopes in Ar
is important for utilizing UAr for dark matter and 0$\nu\beta\beta$ experiments
in terms of its production, transportation, and storage. Ar exposure to cosmic
rays at sea-level is simulated using Geant4 for a given cosmic ray muon,
neutron, and proton energy spectrum. We report the simulated cosmogenic
production rates of $^{39}Ar$, $^{42}Ar$, and other long-lived isotopes at
sea-level from fast neutrons, high energy muons, and high energy protons. Total
production rates of 938.53/kg$_{Ar}\cdot$day and
5.81$\times$10$^{-3}$/kg$_{Ar}\cdot$day for $^{39}$Ar and $^{42}$Ar are found
from our simulation. Utilizing these production rates, we set a time limit of
954 days constrained by the production of $^{39}$Ar for UAr to be on the
surface before it compromises the sensitivity for a dark matter experiment.
Similarly, a time limit of 1702 days constrained by the production of $^{42}$Ar
is found for a 0$\nu\beta\beta$ experiment.
