The US Environmental Protection Agency has set a limit on th

The US Environmental Protection Agency has set a limit on the emission of radon-222 from mill tailings: 0.75 Bq*m^(-2)*s^(-1). For an uncovered pile of tailings of dimensions 35 m x 25 m x 5.0 m, sitting on the ground and emitting radon-222 at the maximum rate allowed, what mass of radon-222 is emitted to the atmosphere per day? The half-life of radon-222 is 3.8 days.

Solution

emission rate of Radon 0.75 Bq/m²/s

Thickness of the tiles is not given, we assume 5mm thick of each

Total area of the tailings = 35.0*25.0*5/5.0e-3

            Production of Radon-222 = 35.0*25.0*5/5.0e-3 *0.75

                                                          = 656.25e+3 /s

           Radon is produced at a constant rate but it decays with its own decay constant

T_1/2 = 3.8 days

decay constant l = 0.693/(3.8*24*3600) /s

                            = 2.11e-6 /s

in a small interval dt

Radon atoms produced = 656.25e+3 dt

Number of radon atoms decay during the interval

                                      = 656.25e+3 *2.11e-6 dt

Number of radon atoms left at the end of the interval

    dN = 656.25e+3 dt - 656.25e+3 *2.11e-6 dt

              = 656.25e+3 (1- 2.11e-6) dt         

Radon accumulates over a period of time, Number of Radon atoms accumulated after an interval of T is obtained by integrating the above expression

N = 656.25e+3 (1- 2.11e-6) T² /2

after T = 24 hrs

N(24hrs) = 328.12e+3(1-2.11e-6)24*3.6e+3

               = 2.835e+10 atoms

Radon molecular weight = 222 gms

Mass of radon accumulated = 222*(2.835e+10 /0.602e-24)

                                              = 1.0455e-11 gms