Another Isotope?

Since it's the case of radioactive decay, it is in Geometric Progression. After the $n^{th}$ hour, i.e at the $(n+1)^{th}$ hour, its mass will be $488.28125mg = 0.48828125g$ .

$a_1 = 500, r = \frac{1}{2}, n = n+1$ $a_n = a_1 r^{n-1}$ $0.48828125 = 500 \times \Big( \frac{1}{2} \Big) ^{(n+1)-1}$ $\frac{0.48828125}{500} = \frac{1}{2^n}$ $\frac{500}{0.48828125} = 2^n$ $2^n = 1024$ $2^n = 2^{10} \Rightarrow \boxed{n = 10}$ Hence after 10 hours, the mass of the radioactive material will be $488.28125mg$