Problem
We have a cubic room of side $10$ m$10\rm\ m$, into which no fresh air has been allowed to flow for a week. We register a specific activity of radon ($Rn-222$)$(^{222}\rm Rn)$ of $50$ Bqm$^{-3}$$50\ \rm Bq\,m^{-3}$. Knowing that $Rn-222$$^{222}\rm Rn$ is a product in the $U-238$$^{238}\rm U$ chain, we would like to find the concentration of $U-238$$^{238}\rm U$ in the walls of this room. We take for granted that the radon diffuses through a $3$ cm$3\rm\ cm$ thick layer of wall.
My attempt
I assume that the activity concentration of the Radonradon is the same as that of the Uraniumuranium from which it's coming. I compute the activity of the Radonradon using $A$ = ($50$ Bqm$^{-3}$)($10^3$m$^3$)$=$ $50 000$ Bq$A = (50\rm\ Bq\,m^{-3})(10^3\ m^3)= 50 000\ Bq$. Then taking one of the four walls, the concentration of Uraniumuranium is given by the activity per unit volume in the thin layer through which the Radonradon diffuses, that is, $C =$ ($50 000$ Bq $)$/($10$ x $10$ x $0.03$ m$^3$)$C = (50 000\ \rm Bq)/(10 \times 10 \times 0.03\ m^3)$.
I think this approach is flawed. Any hint towards a more reasonable solution will be appreciated I think this approach is flawed. Any hint towards a more reasonable solution will be appreciated.
