Step-by-step explanation:
the decay or "half-life" of radioactive particles is really a big joke by nature, in my opinion.
it takes that much time for half of the amount to decay, so, naturally, one wound assume that after a second interval then the other half is gone.
but far from it. no, only the half of the originally remaining half is then gone (the half of a half is 1/2 × 1/2 = 1/4). and after another interval the half of the half of the half is then gone. and so on.
so, this creates a geometric sequence with the common factor (or ratio) if 1/2.
that means every term is created by multiplying the previous term by 1/2.
a.
how many "half-lives" in 1104 days ?
well, with every 138 days such a half-life is over.
so, the answer is how often 138 fits into 1104 :
1104 / 138 = 8
there are 8 "half-lives" of polonium-210 in 1104 days.
b.
how much polonium-210 is in the sample after 1104 days ?
since we have 8 half-lives, we need to multiply the original amount 8 times by 1/2. in other words by 1/2⁸.
2⁸ = 256
so, our calculation is
30 g × 1/256 = 0.1171875 g ≈ 0.12 g
so, the second answer option is correct.
