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?
k = 0.693/t1/2
Then substitute k into the equation below.
ln(No/N) = kt
No = 24
N = solve for this
k from top equation
t = 15,000
Post your work if you get stuck.
Of course the much easier way is to say you go through three half lives so you are left with 1/8 of 24 = 3 grams.
To determine the amount of grams that would be left after 15,000 years, we need to calculate how many half-lives have passed in that time.
Since the half-life of the atom is 5,000 years, we can divide the total time (15,000 years) by the half-life to find the number of half-lives.
15,000 years / 5,000 years = 3 half-lives
Each half-life halves the amount of the atom remaining. Therefore, after three half-lives, the remaining amount will be:
Original amount = 24 grams
First half-life: 24 grams / 2 = 12 grams
Second half-life: 12 grams / 2 = 6 grams
Third half-life: 6 grams / 2 = 3 grams
After 15,000 years, there would be 3 grams of the unstable atom remaining.
To determine how many grams would be left after 15,000 years, we will first need to determine the number of half-lives that have elapsed.
The formula to calculate the number of half-lives elapsed is as follows:
Number of half-lives elapsed = (elapsed time) / (half-life)
In this case, the elapsed time is 15,000 years and the half-life is 5,000 years. Let's calculate the number of half-lives:
Number of half-lives elapsed = 15,000 years / 5,000 years = 3
Now, we can use the number of half-lives elapsed to calculate the remaining amount of the unstable atom using the formula:
Remaining amount = Initial amount * (1/2)^(number of half-lives elapsed)
The initial amount is given as 24 grams. Let's plug in the numbers and calculate the remaining amount:
Remaining amount = 24 grams * (1/2)^3 = 24 grams * (1/8) = 3 grams
Therefore, after 15,000 years, there would be approximately 3 grams of the unstable atom remaining.