3.
Continuous Measurements
During climb or descent of the aircraft the radon concentration is not constant and it is no longer
possible to determine the radon concentration directiy
rrom the filter activity.
Our method allows determination of the concentration
profile by assuming that radioactive equilibrium remains fixed in the air.
The
variation of the number of atoms of each daughter present on the filter is equal
to:
d N, (+)
dt
where q is the air flow, N is the number of atoms of each type and A is the decay
constant for each daughter.
We assume that during the time interval from vo to t that the quantity of
each element reaching the filter is constant and that the equilibrium remains
After integration:
N5(%)
= Ad No (to) + B, Qo(t)
(
N2(t) = Az Nz (ty) + Bz No{tg)
+ C3 Qo(t)
N,(%) = A, N, (to)
C: )
te
established.
~~
jar
= Q;(t) QtAi_y] N;_, (+) AG N;(t)
+ By N3( tg) + C, No(to) + D, Q(t)
where A, B, C, and D are the constant coefficients for the time interval determined
from the initial equations.
The alpha activity of the filter during the time interval from by to t iss
RY (t) = Kap No(t) +A, NC)
where K is a coefficient allowing for the difference in detection efficiency for
polonium-218 and polonium214.
The radon concentration may thus be written:
:
Q2(%) = EEF1 Ago Fal) = MRabaN
a( ty) FAYAN, (to) FAGBANGCEa) tou
+ CyuNalto)
Knowing that at the start of sampling ty = 0, No(0) = 0, N2(0) = 0, and N, 69) = 0,
(@