Theoretical lower limit of mass of phonon and critical mass for matter-dark matter conversion

From Planck's equation for black body radiation and de Broglie's wave-particle duality relation, we can get a relation between the mass of a phonon and frequency of the emitted radiation. From this relation, we get the theoretical lower limit of the mass of a phonon and critical mass for matter-dark matter conversion. The maximum matter density and limit of the string length are also discussed in this respect. It is observed that there is a critical mass of the smallest particle, which is kg, above which we get normal matter and below, the dark matter. It is also observed that if phonon obeys the de Broglie's equation, generation of an electromagnetic radiation of frequency less than 56638721410 Hz is not possible by thermal heating.