Small spherical particles of diameter D = 50 m contain a fluorescent material that, when irradiated with

Small spherical particles of diameter D = 50 μm contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent flow by observing their emitted color.
If the particles are characterized by a density, specific heat, and thermal conductivity of p = 999 kg/m³, k = 1.2 W/m
· K, and c_p = 1200 J/kg ·K, respectively,  determine the time constant of the particles.