Half-Life and Radioactive Decay Concepts

Half-Life Overview

• Short Half-Life:

  • Takes a small amount of time (e.g., microseconds).

  • More dangerous due to rapid decay and high energy release.

• Long Half-Life:

  • Takes a large amount of time (e.g., billions of years).

  • Less dangerous as energy is released gradually.

Factors in Half-Life Calculations

• Total Time: The specific time frame of the decay problem.

• Half Life Time: Duration of half-life for the specific isotope.

• Number of Half Lives (n): Total half-lives that have occurred.

• Starting Mass: Initial amount of parent isotope.

• Ending Mass: Remaining amount of parent isotope post-decay.

Calculating Half Lives

• To find the number of half-lives:

  • Use formulas based on known or unknown variables.

  • Logs help solve for exponents.

Carbon-14 Specifics

• C-14 Half-Life: 5,730 years, decays into Nitrogen-14.

• Example #1: Starting with 200g C-14 for 28,650 years:

  • Calculate n: $n = \frac{28650}{5730} = 5$

  • Ending Mass: $\text{Remaining} = \frac{200g}{2^5} = 6.25g$

• Example #2:

  • Starting 200g, remaining 47.5g, find n:

  • Use $n = \frac{\log(200/47.5)}{\log(2)}$

  • Result: $n = 2.07$ -> Total Time: $2.07 \times 5730 \approx 11861.1 \text{ years}$

Decay Types and Particle Changes

• Decay types involve changes in atomic number and mass:

  • Alpha (2P + 2N): decreases atomic number by 2, mass by 4.

  • Beta (1 e-): increases atomic number by 1.

  • Electron Capture: decreases atomic number by 1.

  • Positron Emission: decreases atomic number by 1, mass unchanged.

Key Point on Half-Life

• Definition: Time required for half of a radioactive isotope to decay into its daughter isotope.

• Precision: Unique, reliable, and does not change for each isotope.