If you have 24 grams of an unstable atom with a half life of 5,000 years, how many grams would be left after 15,000 years
Every 5000 years, the amount goes down by half. There three half-lives in 15,000 years.
24/2^3 = 24/8 = 3g
To determine the amount of grams left after a certain period of time, we can use the half-life formula. The formula is:
N = N0 * (1/2)^(t / T)
Where:
N = the final amount of grams
N0 = the initial amount of grams
t = the time passed
T = the half-life
Given:
N0 = 24 grams
T = 5,000 years
t = 15,000 years
Plugging these values into the formula, we can solve for N:
N = 24 * (1/2)^(15,000 / 5,000)
N = 24 * (1/2)^3
N = 24 * (1/8)
N = 3 grams
Therefore, after 15,000 years, there would be 3 grams of the unstable atom left.
To determine the amount of grams that would be left after 15,000 years, we need to calculate the number of half-life cycles that have occurred within that time frame.
Given that the half-life of the atom is 5,000 years, we can determine the number of half-life cycles within 15,000 years by dividing the total time (15,000 years) by the length of each half-life cycle (5,000 years).
In this case, 15,000 years divided by 5,000 years gives us 3 half-life cycles.
Each half-life cycle reduces the initial amount of the atom by half. So, after the first half-life cycle, there would be half of the initial amount remaining. After the second half-life cycle, there would be half of that remaining, and after the third half-life cycle, there would again be half of that remaining.
Therefore, if we start with 24 grams and go through three half-life cycles, the amount of the unstable atom that would be left after 15,000 years would be:
24 grams × (1/2) × (1/2) × (1/2) = 3 grams.
So, after 15,000 years, there would be approximately 3 grams remaining of the unstable atom.