A moon rock collected by a U.S. Apollo mission is estimated to be 4.50 billion years old by uranium/lead dating. Assuming that the rock did not contain any lead when it was formed, what is the current mass of 206Pb per 1.150 g of 238U in the rock? The half-life of 238U is t1/2 = 4.47 × 109 years.
What is t? Everytime I put 4.50*10^12 for t then I take the e of it I get an error and if I do it negative I get 0. Don't understand this problem at all.
Ah, uranium/lead dating, the ultimate matchmaker for rocks! Let's calculate the current mass of 206Pb per 1.150 g of 238U in the moon rock.
To begin, we need to determine how many half-lives have passed since the rock was formed. We can do this by dividing the age of the moon rock by the half-life of uranium-238:
Age of the moon rock = 4.50 billion years
Half-life of uranium-238 = 4.47 × 10^9 years
Number of half-lives = Age of the moon rock / Half-life of uranium-238
= 4.50 × 10^9 years / 4.47 × 10^9 years
≈ 1.0071 half-lives
So, around 1.0071 half-lives have passed since the rock formed. Since each half-life reduces the amount of 238U by half, we can calculate the current mass of 238U by dividing the original mass by 2 raised to the power of the number of half-lives:
Current mass of 238U = (Original mass of 238U) / (2^(Number of half-lives))
Now, let's solve for the current mass of 206Pb. We know that uranium-238 decays into lead-206, so the current mass of 206Pb will be equal to the original mass of 238U minus the current mass of 238U:
Current mass of 206Pb = (Original mass of 238U) - (Current mass of 238U)
To find the current mass of 206Pb per 1.150 g of 238U, we'll divide the current mass of 206Pb by 1.150 g:
Mass ratio of 206Pb to 238U = (Current mass of 206Pb) / (1.150 g)
Voila! With these calculations, you should be able to determine the current mass of 206Pb per 1.150 g of 238U in the moon rock. Rock on with your calculations!
To solve this problem, we can use the concept of radioactive decay and the decay equation for uranium-238 (238U) to lead-206 (206Pb).
The decay equation for 238U is:
238U --> 206Pb + 8 alpha particles (α)
The half-life of 238U is t1/2 = 4.47 × 10^9 years. This means that half of the 238U will decay into 206Pb in this time period.
1. Let's calculate the number of half-lives since the rock was formed:
Number of half-lives = Age of rock / Half-life
Number of half-lives = 4.50 billion years / 4.47 billion years
Number of half-lives ≈ 1
2. Since only one half-life has passed, half of the 238U has decayed into 206Pb.
Therefore, the current mass of 206Pb is half of the initial mass of 238U.
3. We can calculate the initial mass of 238U using the given information.
Initial mass of 238U = 1.150 g
4. The current mass of 206Pb per 1.150 g of 238U can be calculated as follows:
Current mass of 206Pb = (1/2) x 1.150 g
Current mass of 206Pb = 0.575 g
Therefore, the current mass of 206Pb per 1.150 g of 238U in the rock is 0.575 g.
To solve this problem, we need to use the concept of radioactive decay and the half-life of uranium-238.
First, let's determine how many half-lives have passed since the rock was formed. Given that the half-life of uranium-238 (238U) is 4.47 × 10^9 years, we can find the number of half-lives using the following formula:
Number of half-lives = Age of rock / Half-life
Substituting the values:
Number of half-lives = 4.50 × 10^9 years / 4.47 × 10^9 years
Number of half-lives = 1.0089
This indicates that approximately 1.0089 half-lives have occurred since the rock was formed.
Next, we need to find the amount of lead-206 (206Pb) that has been produced during these half-lives. Since each half-life of uranium-238 produces one half-life's worth of lead-206, we can calculate:
Amount of 206Pb produced = Initial amount of 238U / 2^number of half-lives
Substituting the values and assuming the initial amount of 238U is 1.150 g:
Amount of 206Pb produced = 1.150 g / 2^(1.0089)
Amount of 206Pb produced = 1.150 g / 1.997
Amount of 206Pb produced ≈ 0.576 g
Therefore, the current mass of 206Pb per 1.150 g of 238U in the rock is approximately 0.576 g.
I would do this.
k = 0.693/t1/2
Then ln(No/N) = kt
You know N is 1.150g U and k from above. solve for No which gives you grams U you started with.
g U initially - g U now = g U changed to Pb.
Then convert g U convert to g Pb 206.
g U changed x (206/238) = ? Pb now.