Half-Life and Decay Constant
The half-life
Definition
The half-life of a radioactive substance is the time required for the number of undecayed nuclei, or equivalently its activity, to fall to half its initial value.
After Several Half-Lives
Decay law: N=N₀e-λt At: t=T₁/₂ we have: N=N₀/2 Therefore: 12=e(-λT₁/₂) Taking logarithms: T₁/₂ = ln2/λ or: T₁/₂≈0.693λ After `n` half-lives: **N=N₀(12)ⁿ Likewise: R=R₀(12)ⁿ** Examples: 1 half-life → `12` 2 → `14` 3 → `18` 4 → `116`
Formula / Key Relation
**T₁/₂=ln2/λ ≈0.693λ**
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Half-Life and Decay Constant
Sticky Notes · Quick Revision
`T½=0.693/λ`
- 1 T½ → 12
- 2 T½ → 14
- 3 T½ → 18
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- Half-life and decay constant are inversely related.
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