Gas lanterns used on camping trips have mantles (small lacy bags that give off light) made from a rayon mesh impregnated with thorium and other materials. Thorium is used, even though it is radioactive, because it forms an oxide that can withstand being incandescent for long periods of time. Almost all natural thorium is 23290Th, which has a half-life of 1.405×1010y.
(A) A typical mantle contains 345 mg of thorium. What is the activity of the mantle?
(B) If the half-life of thorium had been double its actual value, by what factor would the activity of a mantle be changed?