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Half-life and decay constant calculator
Nuclear and particles
Links the half-life of a radioactive isotope to its decay constant.
T½ = ln 2 / λ
This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equationT½ = ln 2 / λ
- Substitute the valuesT½ = ln 2 ÷ 0.0693
- CalculateT½ = 10.0021 s
- Give the answer to 3 significant figuresT½ = 10.0 s
Worked example
Find T½, the half-life. Given: decay constant λ = 0.0693 s⁻¹.
- Write the equationT½ = ln 2 / λ
- Substitute the valuesT½ = ln 2 ÷ 0.0693
- CalculateT½ = 10.0021 s
- Give the answer to 3 significant figuresT½ = 10.0 s
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| T½ | Half-life | s |
| λ | Decay constant | s⁻¹ |
Half-life and decay constant: rearranged
- To find half-life: T½ = ln 2 / λ
- To find decay constant: λ = ln 2 / T½
Exam tip
ln 2 is about 0.693. Keep the time unit the same as the unit in λ.
Common questions
What is the formula for half-life and decay constant?
The equation is T½ = ln 2 / λ, where T½ is the half-life (s); λ is the decay constant (s⁻¹).
What units should I use for half-life and decay constant?
In SI units: half-life in s, decay constant in s⁻¹. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange T½ = ln 2 / λ?
Rearranging gives these forms: to find half-life: T½ = ln 2 / λ. to find decay constant: λ = ln 2 / T½.
Practise half-life and decay constant questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
More nuclear and particles equations: Photon energy, Photon energy from wavelength, Photoelectric equation, de Broglie wavelength, Radioactive decay and half-life, Activity and decay constant, Mass–energy equivalence. See the full list on the a-level physics equation calculator page.