Decay Law & Half-Life

N(t) = N₀ exp(−λt).

Concept

Decay Law & Half-Life is a foundational idea in this chapter. The defining relationship is:

$T_{1/2} = \ln 2/\lambda$

Mean life τ = 1/λ. Activity A = λN.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $T_{1/2} = \ln 2/\lambda$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.