A sample 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?

The sample have passed 4 half lives after the sample was originally formed.

Explanation:

Half life is the time required to calculate the amount of a sample to half its value.

To calculate number of half- lives , the equation is used

(1/2)^n =x

where, n is  number of half -lives

              x is the remained fraction of a sample

we have to find n, so we can do it by calculating x. if sample contains 10.5 g of the radioisotope pb-212 and 157.5 g of daughter isotope

then the total is

157.5 g + 10.5 g = 168 g of the sample

Out of this 168 g, 10.5 g remained of the radioisotope pb-212.

The fraction is

10.5 ÷ 168 = 0.0625

x = 0.0625

(1/2)^n = x

n * log (1/2) = log (x)

n * log (0.5) = log (x)

n =

n =

n =

n= 4

Thus, the number of half lives is 4