If you started with 100 grams of Potassium-40 how much would reamin Potassium-40 after 3.9 x 10 to the 9th years?
The half life of K-40 is 1.3*10^9 years.
That is something they should have told you, or which you have to look up.
3.9*10^9 years (the approximate age of the earth) is three half lives.
100g*(1/2)^3 = ??
82437097235
To calculate the remaining amount of Potassium-40 after 3.9 x 10^9 years, we need to understand the concept of half-life.
The half-life of Potassium-40 is approximately 1.28 billion years. This means that after every 1.28 billion years, half of the original amount of Potassium-40 will decay.
We can calculate the number of half-lives by dividing the total time (3.9 x 10^9 years) by the half-life (1.28 x 10^9 years):
Number of half-lives = (Total time) / (Half-life) = (3.9 x 10^9 years) / (1.28 x 10^9 years) = 3.046875
Next, we need to calculate the remaining fraction of Potassium-40 after 3.046875 half-lives. This can be done by raising 0.5 (representing half) to the power of the number of half-lives:
Remaining fraction = 0.5^(Number of half-lives) = 0.5^(3.046875) ≈ 0.213
Finally, we can calculate the remaining amount of Potassium-40 by multiplying the remaining fraction by the original amount:
Remaining amount = (Remaining fraction) x (Original amount)
= 0.213 x 100 grams
= 21.3 grams
Therefore, approximately 21.3 grams of Potassium-40 would remain after 3.9 x 10^9 years.