Final answer:
The half-life of the radioactive substance is 1 year. After 11 years, approximately 0.0059 g of the substance will be present.
Step-by-step explanation:
The amount of a radioactive substance remaining after a certain amount of time can be calculated using the half-life of the substance. The half-life is the time it takes for half of the radioactive material to decay. In this case, if 12 g of the substance is present initially and after 8 years only 6 g remain, we can calculate the half-life of the substance.
Let's assume that the half-life of the substance is x years.
After the first half-life, 6 g remain, which is half of the initial amount:
12 g * (1/2) = 6 g
So, after x years, half of the substance decays:
12 g * (1/2) * (1/2) * (1/2) ... (repeated x times) = 6 g
To find x, we can set up the equation:
12 g * (1/2)^x = 6 g
Rewriting the equation in exponential form:
(1/2)^x = 6 g / 12 g = 1/2
x = log base (1/2) of (1/2) = 1
So, the half-life of the substance is 1 year.
After 11 years, we can calculate the amount of substance remaining:
12 g * (1/2)^(11/1) = 12 g * (1/2)^11 = 12 g * (1/2048) = 0.0059 g (rounded to 4 decimal places)
Therefore, after 11 years, approximately 0.0059 g of the substance will be present.