Someone plans to float a small, totally absorbing sphere $0\mathrm{.}502$ m above an isotropic point source of light, so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere's density is $20\mathrm{.}4\frac{g}{c}{m}^3,$ and its radius is $2\mathrm{.}04$ mm $.($a$)$ What power would be required of the light source? $($b$)$ Even if such a source were made, would the support of the sphere be unstable? Assume that the speed of light is $2\mathrm{.}998{10}^8\frac{m}{s}.$

$($a$)$ Number $$ Units $$

$($b$)$