Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 100 years?
Sorry, Matt.
To find the percentage of radioactive radium that remains after 100 years, we can use the formula for exponential decay:
Amount remaining = Initial amount * (1/2)^(t / half-life)
Where:
- Initial amount is the given amount of radium
- t is the time in years
- Half-life is the time it takes for the radium to decay by half
In this case, we are given that the half-life of radium is approximately 1599 years. Let's assume we start with 100 grams of radium.
Amount remaining after 100 years = 100 grams * (1/2)^(100 / 1599)
Using a calculator, we can compute this value:
Amount remaining after 100 years = 100 * (0.5)^(100 / 1599) ≈ 94.021 grams
To find the percentage, we divide the amount remaining by the initial amount and multiply by 100:
Percentage remaining = (Amount remaining / Initial amount) * 100
Percentage remaining = (94.021 / 100) * 100 ≈ 94.021%
Therefore, approximately 94.021% of the given amount of radioactive radium remains after 100 years.
To determine what percent of radioactive radium remains after 100 years, we can use the concept of half-life.
The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay. In this case, the half-life of radium is approximately 1599 years.
To find the percent remaining after 100 years, we need to calculate how many half-lives have occurred in that time period.
Since the half-life of radium is 1599 years, we divide 100 years by 1599 years to determine the number of half-lives:
Number of half-lives = 100 years / 1599 years
Number of half-lives ≈ 0.06253
This tells us that approximately 0.06253 half-lives have occurred in 100 years.
To calculate the percentage remaining, we raise 0.5 (representing the remaining 50%) to the power of the number of half-lives:
Percent remaining = (0.5 ^ number of half-lives) * 100
Substituting the value of the number of half-lives, we get:
Percent remaining ≈ (0.5 ^ 0.06253) * 100
Using a calculator, we find that 0.5 raised to the power of 0.06253 is approximately 0.974.
Therefore, the percent of radium remaining after 100 years is about 0.974 * 100, which is approximately 97.4%.
So, roughly 97.4% of the initial amount of radium remains after 100 years.
left=original*e^(.692t/1599)
left/original= e^ ( )
put in t=100, and solve.