Formula explainer. Open the full deep dive
Quantum Formula

What is Half-Life Decay?

Radioactive nuclei decay at a rate proportional to the number remaining, leading to exponential decrease over time.

Formula: N(t) = N_0 e^{-\lambda t}

Plain-English Meaning

Radioactive nuclei decay at a rate proportional to the number remaining, leading to exponential decrease over time.

When a quantum question feels ambiguous, translating it into state, observable, probability, and evolution language usually clarifies the answer.

Deeper Explanation

Radioactive nuclei decay at a rate proportional to the number remaining, leading to exponential decrease over time.

Worked Example

Problem: Carbon-14 has t₁/₂ = 5730 years. What fraction remains after 11,460 years?

  • 11,460 = 2 × 5730 → exactly 2 half-lives
  • Fraction = (1/2)² = 1/4 = 25%

Result: 25% of original C-14 remains

At A Glance

Category: Quantum

Levels covered:

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.