Geochronology

Step 1: Understanding the decay process.
The radioactive decay of uranium-238 ( ) follows a chain of alpha and beta decays until it forms stable lead-206 ( ). To calculate the number of alpha particles emitted, we look at the decay chain.

Step 2: Analyzing the decay chain.
The decay of to involves the emission of 8 alpha particles. This is because decays to , and through subsequent decays, eventually leads to , with 8 total alpha emissions.

Step 3: Conclusion.
The number of alpha particles emitted is 8.

Step 1: Understanding the data.
Total vertical distance between the dated horizons = 10 m – 0 m = 10 m. Time difference between 77 Ma and 76 Ma = 1 Ma.
Step 2: Calculating sedimentation rate.
Sedimentation rate = 10 m per 1 Ma = 10 m/Ma.
Step 3: Calculating age at 7 m height.
From the base (77 Ma) to 7 m height: Time elapsed = 7 m ÷ 10 m/Ma = 0.7 Ma.
Therefore, age = 77 – 0.7 = 76.3 Ma.
Step 4: Conclusion.
The extinction event occurred at approximately 76.3 Ma.

Step 1: Radioactive decay relation.
where = final activity, = initial activity, = time, and = decay constant.
Step 2: Substitute known values.
Step 3: Calculate half-life.
Step 4: Conclusion.
The half-life of the mineral ≈ 118.3 minutes.