1) Conversion of H₂S Concentration from mg/m³ to ppm
The Occupational Safety and Health Administration (OSHA) ceiling limit for hydrogen sulfide (H₂S) is 20
ppm for general industry. To determine if a reading of 35 mg/m³ exceeds this limit, we must convert the
concentration from mg/m³ to ppm. The molecular weight of H₂S is calculated as follows:

Atomic mass of H = 1.007

Atomic mass of S = 32.065

Molecular weight of H₂S = (2 × 1.007) + 32.065 = 34.079 g/mol
The conversion formula from mg/m³ to ppm is:
ppm=mg/m3×24.45Molecular Weightppm=Molecular Weightmg/m3×24.45
Where 24.45 is the molar volume of an ideal gas at standard temperature and pressure (25°C and 1
atm). Substituting the values:
ppm=35 mg/m3×24.4534.079 g/mol≈25.1 ppmppm=34.079g/mol35mg/m3×24.45≈25.1ppm
Since 25.1 ppm exceeds the OSHA ceiling limit of 20 ppm, this level is above the permissible limit (OSHA,
2023).
2) Inverse Square Law for Radiation Intensity
The inverse square law states that radiation intensity decreases with the square of the distance from the
source. The formula is:
I1×d12=I2×d22I1×d12=I2×d22
Where:

I1I1 = Initial intensity (3.125 R/min)

d1d1 = Initial distance (1 foot)

I2I2 = Final intensity (5 mR/min = 0.005 R/min)

d2d2 = Final distance (unknown)
Rearranging the formula to solve for d2d2:
d2=I1×d12I2=3.125×120.005=625=25 feetd2=I2I1×d12=0.0053.125×12=625=25feet
Thus, the distance to the 5 mR/min boundary is 25 feet (NRC, 2023).
References

OSHA. (2023). Occupational Safety and Health Standards.

NRC. (2023). Radiation Protection Guidelines.