Complete the table for the radioactive isotope. (Round your answer to two decimal places.)
Isotope: 239Pu
Half-life (years): 24,100
Initial Quantity: g
Amount After 1000 Years: 0.6
Oh, radioactive isotopes, they're always decaying and causing trouble! But don't worry, I'll help you complete that table and bring some humor to this scientific affair.
Isotope: 239Pu
Half-life (years): 24,100
Initial Quantity: Assumed to be hilariously large
Amount After 1000 Years: 0.6 (Which is definitely not a half-life of a stand-up comedian)
Now, let's calculate the initial quantity of our funny 239Pu isotope. Since we're dealing with half-life, we can use the equation:
Final Amount = Initial Amount * (1/2)^(Time / Half-life)
Substituting the given values, we have:
0.6 = Initial Amount * (1/2)^(1000 / 24100)
Now, let's solve for the Initial Amount:
Initial Amount = 0.6 / (1/2)^(1000 / 24100)
Calculating this using my little clown calculator, we find:
Initial Amount ≈ 0.564 grams
So, the initial quantity of our radioactive isotope 239Pu is approximately 0.564 grams. And remember, when it comes to half-lives and isotopes, there's always room for a good radioactive joke!
To complete the table, we need to find the initial quantity of the radioactive isotope.
The formula to calculate the amount of a radioactive isotope remaining after a certain number of years is:
Amount = Initial Quantity * (1/2)^(Years / Half-life)
Given that the half-life of isotope 239Pu is 24,100 years and the amount after 1000 years is 0.6 g, we can plug these values into the formula to solve for the Initial Quantity.
0.6 = Initial Quantity * (1/2)^(1000 / 24,100)
To solve for the Initial Quantity, we can rearrange the equation:
Initial Quantity = 0.6 / (1/2)^(1000 / 24,100)
Now, let's calculate the Initial Quantity using a calculator:
Initial Quantity = 0.6 / (1/2)^(1000 / 24,100)
≈ 0.6 / 0.9783
≈ 0.6136 g
Therefore, the initial quantity of the radioactive isotope is approximately 0.6136 grams.
To complete the table for the radioactive isotope 239Pu, we need to find the initial quantity of the isotope.
The half-life of 239Pu is given as 24,100 years, which means that every 24,100 years, the quantity of the isotope is halved.
We know that after 1000 years, the amount of 239Pu remaining is 0.6 g. Using this information, we can set up the following equation:
Amount After t Years = Initial Quantity * (1/2)^(t / Half-life)
Let's plug in the numbers we have:
0.6 = Initial Quantity * (1/2)^(1000 / 24100)
To solve for the Initial Quantity, we need to isolate it on one side of the equation. We can start by dividing both sides of the equation by (1/2)^(1000 / 24100):
Initial Quantity = 0.6 / (1/2)^(1000 / 24100)
Now, let's calculate the expression on the right side using a calculator or a computer program. After rounding the answer to two decimal places, we can fill in the value in the table for the Initial Quantity.
amount = (initital value) (1/2)^(t/24100)
sub in : amount = .6, t = 1000
I assume you want to find the initial value