Question

Problem 3. Consider an enclosed area inside a uranium mine with dimensions of 5 × 4× 3 m3. The walls are emitting Radon-222 at a rate of 0.1 atoms/(cm2·s). a) Derive differential equation describing number of Rn-222 atoms in this enclosed space, considering its emission from the walls, radioactive decay, and ventilation. b) Determine equilibrium concentration of Rn-222 in this space without ventilation in pCi/L. c) What should be air ventilation flow rate in L/s to maintain activity below 5 pCi/L?

Answer 1

B) 430 Pci/L

C) F = 1.05 * 10 ^13 L/s

Step-by-step explanation:

Given data :

enclosed area dimensions : 5 * 4 * 3 m^3

emission of Radon-22 through walls = 0.1 atoms/(cm^2.s)

first we will have to determine the total surface area of the enclosed area

= 2 lb + 2 bh + 2 lh

= 2( 5*4 ) + 2( 4*3 ) + 2 ( 5*3 ) = 9.4 * 10^5 cm^2

next we determine the production rate ( P )

p = 0.1 atoms/(cm^2.s) * 9.4 * 10^5 cm^2 = 9.4 * 10^5 atoms/s

determine production rate per volume

production rate / space volume = 9.4 * 10^5 / ( 5*4*3 )

= 9.4 * 10^5 / (60 * 10^3) L

= 16 atoms/ L

attached below is the remaining part of the solution