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!