Using Uranium/Lead Dating to Estimate the Age of a Rock
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Q1. A meteor contains 0.556 g of Pb-206 to every 1.00 g of U-238. Assuming that the meteor did not contain any Pb-206 at the time of its formation, determine the age of the meteor. Uranium-238 decays to lead-206 with a half-life of 4.5 billion years.
What you'll need:
Half-life of uranium: (4.5×〖10〗^9 years)
Q2. A rock contains Pb-206 to U-238 mass ratio of 0.145:1.00. Assuming that the rock did not contain any Pb-206 at the time of its formation, determine the age of the rock.
SORT You are given the current masses of Pb-206 and U-238 in a rock and asked to find its age. You are also given the half-life of U-238.
STRATEGIZE You use the integrated rate law (Equation 19.3) to solve this problem. However, you must first determine the value of the rate constant (k) from the half-life expression.
Before substituting into the integrated rate law, you also need the ratio of the current amount of U-238 to the original amount (Nt/N0). The current mass of uranium is simply 1.00 g. The initial mass includes the current mass (1.00 g) plus the mass that has decayed into lead-206, which can be determined from the current mass of Pb-206.
Use the value of the rate constant and the initial and current amounts of U-238 along with integrated rate law to find t.
SOLVE Follow your plan. Begin by finding the rate constant from the half-life.
Determine the mass in grams of U-238 that is required to form the given mass of Pb-206.
Substitute the rate constant and the initial and current masses of U-238 into the integrated rate law and solve for t. (The initial mass of U-238 is the sum of the current mass and the mass that is required to form the given mass of Pb-206.)
CHECK The units of the answer are correct. The magnitude of the answer is about 3.2 billion years, which is less than one half-life. This value is reasonable given that less than half of the uranium has decayed into lead.
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Q1. A meteor contains 0.556 g of Pb-206 to every 1.00 g of U-238. Assuming that the meteor did not contain any Pb-206 at the time of its formation, determine the age of the meteor. Uranium-238 decays to lead-206 with a half-life of 4.5 billion years.
What you'll need:
Half-life of uranium: (4.5×〖10〗^9 years)
Q2. A rock contains Pb-206 to U-238 mass ratio of 0.145:1.00. Assuming that the rock did not contain any Pb-206 at the time of its formation, determine the age of the rock.
SORT You are given the current masses of Pb-206 and U-238 in a rock and asked to find its age. You are also given the half-life of U-238.
STRATEGIZE You use the integrated rate law (Equation 19.3) to solve this problem. However, you must first determine the value of the rate constant (k) from the half-life expression.
Before substituting into the integrated rate law, you also need the ratio of the current amount of U-238 to the original amount (Nt/N0). The current mass of uranium is simply 1.00 g. The initial mass includes the current mass (1.00 g) plus the mass that has decayed into lead-206, which can be determined from the current mass of Pb-206.
Use the value of the rate constant and the initial and current amounts of U-238 along with integrated rate law to find t.
SOLVE Follow your plan. Begin by finding the rate constant from the half-life.
Determine the mass in grams of U-238 that is required to form the given mass of Pb-206.
Substitute the rate constant and the initial and current masses of U-238 into the integrated rate law and solve for t. (The initial mass of U-238 is the sum of the current mass and the mass that is required to form the given mass of Pb-206.)
CHECK The units of the answer are correct. The magnitude of the answer is about 3.2 billion years, which is less than one half-life. This value is reasonable given that less than half of the uranium has decayed into lead.
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