Spherical molten metal droplets are quenched during flight in a vacuum chamber, the walls of which are assumed to be a black body at 25C. Since there is no surrounding fluid (only vacuum), heat is transferred from the particles to the surroundings by radiation. A minimum cooling rate of 106K/s is required in order to obtain an amorphous alloy (of a particular composition). This cooling rate should be calculated at the melting point of the metal, right after all the droplet has solidified. The alloy has the physical properties listed at the end of the problem. Please estimate the maximum radius that will cool sufficiently quickly to meet our requirement. It is reasonable to assume for this problem that the temperature throughout the metal particle is uniform