If a radioactive isotope has a half life of 10 years and you start with 100 grams what is the fraction left, percentage left, and amount of original in grams
I would like for you to explain how to do it not tell me the answer that's the question
jhggyj
To find the fraction and percentage of a radioactive isotope remaining after a given time, as well as the amount in grams, we can use the concept of radioactive decay and the half-life.
The half-life of a radioactive isotope is the time it takes for half of the initial quantity to decay. In this case, the half-life is 10 years.
To find the fraction remaining, divide the time elapsed by the half-life. In this case, let's assume that 20 years have passed. Dividing 20 years by the 10-year half-life gives us:
20 years / 10 years = 2
So, after 20 years, there have been two half-lives.
To calculate the fraction remaining, raise 1/2 to the power of the number of half-lives. In this example, since there have been two half-lives, the fraction remaining can be calculated as:
(1/2) raised to the power of 2: (1/2)² = 1/4
Therefore, after 20 years, 1/4 (or 25%) of the original radioactive isotope remains.
To determine the amount of the isotope remaining in grams, multiply the fraction remaining (1/4 or 0.25) by the initial quantity. In this case, the initial quantity is 100 grams:
0.25 * 100 grams = 25 grams
Hence, after 20 years, there would be 25 grams of the original 100 grams remaining.
To summarize:
- Fraction remaining = (1/2) raised to the power of the number of half-lives
- Percentage remaining = Fraction remaining * 100%
- Amount remaining in grams = Fraction remaining * initial quantity in grams