A Mathematical Model for a Radon Detection Method Based on Carbon Nanotube Sensor

Abstract

This article is proposing a mathematical model as a basis for radon detection by measurement alpha particle concentration with a carbon nanotubes-based sensor. The working principle at the basis of the mathematical model of the presented sensor is based on the fact that, the concentration of alpha particle in the air is a linear function of radon concentration. The collision between each alpha particle and the attachment of alpha particle to the carbon nanotube, changes the nanotube's own oscillation frequency. After activation, the carbon nanotubes oscillations in frequency depends on their own geometrical dimensions and their mechano-electrical properties. The initial oscillation frequencies spectra of the matrix of carbon nanotube with the same geometrical dimension is compared with the oscillation frequency spectra collected after the sensor is exposed to air sample. Based on their relative frequency variations of the recorded spectra, the radon concentration is evaluated. Radon concentration is determined on the bases of the linear relationship between its concentration and the alpha particles one. According to these theoretical assumptions, the use of carbon nanotubes sensor appears to be suitable for radon concentration measurement with the advantages to be a reusable and a low cost solution.