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Half-life and Decay Constant
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.
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Half-life and Decay Constant
What is it?
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.
In simple words
- Half-life and decay constant are inversely related.
Recommended for Class 12
Full school-level explanation
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**
Remember
- N=N₀(12)ⁿ
- R=R₀(12)ⁿ
- T₁/₂=ln2/λ
- ≈0.693λ
Deeper understanding
Go deeper on Half-life and Decay Constant: connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
`T½=0.693λ`
Exam focus
Quick revision
- N=N₀(12)ⁿ
- R=R₀(12)ⁿ
- T₁/₂=ln2/λ
- ≈0.693λ
- After Several Half-Lives: Decay law: N=N₀e-λt At: t=T₁/₂ we have: N=N₀/2 Therefore: 12=e(-λT₁/₂) Ta
- Formula / Key Relation: **T₁/₂=ln2/λ** **≈0.693λ**
For long answers on Half-life and Decay Constant: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- N=N₀(12)ⁿ
- R=R₀(12)ⁿ
- T₁/₂=ln2/λ
- ≈0.693λ
Important formulas
- N=N₀(12)ⁿ
- R=R₀(12)ⁿ
- T₁/₂=ln2/λ
Common exam traps
- Do not say all radioactive atoms decay exactly after one half-life.
- Half-life describes a population statistically.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not say all radioactive atoms decay exactly after one half-life.
- Mistake
Half-life describes a population statistically.
- Mistake
Do not say all radioactive atoms decay exactly after one half-life.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
N=N₀(12)ⁿ
R=R₀(12)ⁿ
T₁/₂=ln2/λ
≈0.693λ
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
N=N₀(12)ⁿ
- 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
- Formula
- N=N₀(12)ⁿ
- Critical warning
- Do not say all radioactive atoms decay exactly after one half-life.
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Exam Practice
Define
Q1. Define Half-life and Decay Constant.
Explain
Q2. Explain: After Several Half-Lives.
Example
Q3. Give one clear example of Half-life and Decay Constant and say why it fits.
Mistake
Q4. State one common mistake students make about Half-life and Decay Constant.
Exam note
Q5. Write a short exam note on Half-life and Decay Constant: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.