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Activity and decay constant calculator

A-level Nuclear and particles

The activity is the number of decays per second, found from the decay constant and the number of nuclei.

A = λ N

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

9.20 × 107 Bq
s⁻¹

Working

  1. Write the equation
    A = λ N
  2. Substitute the values
    A = 0.0023 × (4 × 1010)
  3. Calculate
    A = 9.2 × 107 Bq
  4. Give the answer to 3 significant figures
    A = 9.20 × 107 Bq

Worked example

Find A, the activity. Given: decay constant λ = 0.00230 s⁻¹; number of undecayed nuclei N = 4.00 × 10¹⁰.

  1. Write the equation
    A = λ N
  2. Substitute the values
    A = 0.0023 × (4 × 1010)
  3. Calculate
    A = 9.2 × 107 Bq
  4. Give the answer to 3 significant figures
    A = 9.20 × 107 Bq

Symbols and units

SymbolQuantitySI unit
AActivityBq
λDecay constants⁻¹
NNumber of undecayed nucleino unit

Activity and decay constant: rearranged

  • To find activity: A = λ N
  • To find decay constant: λ = A / N
  • To find number of undecayed nuclei: N = A / λ

Exam tip

Activity is in becquerel, which is decays per second. N is the number of nuclei present now.

Common questions

What is the formula for activity and decay constant?

The equation is A = λ N, where A is the activity (Bq); λ is the decay constant (s⁻¹); N is the number of undecayed nuclei.

What units should I use for activity and decay constant?

In SI units: activity in Bq, decay constant in s⁻¹, number of undecayed nuclei in no unit (a ratio). The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange A = λ N?

Rearranging gives these forms: to find activity: A = λ N. to find decay constant: λ = A / N. to find number of undecayed nuclei: N = A / λ.

Practise activity and decay constant questions

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Related

More nuclear and particles equations: Photon energy, Photon energy from wavelength, Photoelectric equation, de Broglie wavelength, Radioactive decay and half-life, Half-life and decay constant, Mass–energy equivalence. See the full list on the a-level physics equation calculator page.