Problem

We have a cubic room of side $10$ m, into which no fresh air has been allowed to flow for a week. We register a specific activity of radon ($Rn-222$) of $50$ Bqm$^{-3}$. Knowing that $Rn-222$ is a product in the $U-238$ chain, we would like to find the concentration of $U-238$ in the walls of this room. We take for granted that the radon diffuses through a $3$ cm thick layer of wall.

My attempt

I assume that the activity concentration of the Radon is the same as that of the Uranium from which it's coming. I compute the activity of the Radon using $A$ = ($50$ Bqm$^{-3}$)($10^3$m$^3$)$=$ $50 000$ Bq. Then taking one of the four walls, the concentration of Uranium is given by the activity per unit volume in the thin layer through which the Radon diffuses, that is, $C =$ ($50 000$ Bq $)$/($10$ x $10$ x $0.03$ m$^3$)

I think this approach is flawed. Any hint towards a more reasonable solution will be appreciated