Asample contains 10.5 g of the radioisotope pb-212 and 157.5 g of its daughter isotope, bi-212. how many half-lives have passed since the sample originally formed?
4
14
15
147.5

The answer is 4.

Half-life is the time required for the amount of a sample to half its value.
To calculate number of half-lives, we will use the following equation:

where:
n - a number of half-lives
x - a remained fraction of a sample

We do not know n and x.
n=?
But, we can calculate x (a remained fraction of a sample). If sample contains 10.5 g of the radioisotope Pb-212 and 157.5 g of its daughter isotope, Bi-212, there is in total 157.5 g + 10.5 g = 168 g of the sample. Of these 168 g, 10.5 g remained of the radioisotope Pb-212. The fraction is 10.5 ÷ 168 = 0.0625.
Thus, x = 0.0625







 


Therefore, the number of half-lives is 4.