Why can a radioactive material affect photographic film even though the film is well wrapped in black paper?

According to the definition of half-life, the mass of the radioactive isotope halfs its mass after each half-life, which means the remaining mass is always half the amount of the previous mass. 

Therefore, after the 1st half-life, there is (190/2) g left; after the 2nd half-life, there is (190/2)/2 g left; so on and so forth.  After the 6th half-life, there is 190/(2*2*2*2*2*2) g = 190g/64 = 2.97 g left.

So 2.97 g of this radioactive isotope will be left after 6 half-lives.