Nuclear Decay Calculator

The Nuclear Decay Calculator will calculate the:

number of undecayed atomic nuclei as a function of time in a sample when the initial number and half-life are known

Nuclear Decay Calculator
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Calculator Precision (Decimal Places)
Initial number of atomic nuclei (N₀)
Half-life of radioactive element (T_1/2) s
Time elapsed since the beginning of process (t) s
∞ Real Number Results∑ Scientific Number Results

Nuclear Decay Calculator Results (detailed calculations and formula below)
Number of undecayed particles in the sample as a function of time elapsed calculation
∞ Real Number Results∑ Scientific Number Results
The Number of undecayed particles in the sample as a function of time elapsed N(t) is
N(t) = N₀ ∙ e^{- ln 2/T_1/2 ∙ t} N(t) = ∙ e^{- ln 2/ ∙} N(t) = ∙ e^{- ∙} N(t) = ∙ e N(t) = ∙ N(t) =
Nuclear Decay Calculator Input Values
Initial number of atomic nuclei (N₀)
Half-life of radioactive element (T_1/2) s [second]
Time elapsed since the beginning of process (t) s [second]

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each nuclear decay calculation, the Nuclear Decay Calculator will automatically calculate the results and update the Physics formula elements with each element of the nuclear decay calculation. You can then email or print this nuclear decay calculation as required for later use.

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Discover Physics with free Physics Revision Notes and Physics Calculator: Nuclear Decay. This image shows the properties and nuclear decay formula for the Nuclear Decay. The Nuclear Decay Calculator will calculate the number of undecayed atomic nuclei as a function of time in a sample when the initial number and half-life are known

What is Nuclear Decay?

Nuclear decay, also known as radioactive decay, is a key concept in nuclear physics and chemistry. It is a process where an unstable atomic nucleus loses energy by emitting radiation in the form of alpha, beta, or gamma rays. This decay, or transformation, results in the atom changing into another element or a different isotope of the same element.

The nucleus of an atom is composed of protons and neutrons, collectively known as nucleons. In certain isotopes, the balance between these nucleons is unstable, leading to nuclear decay as the atom seeks to reach a more stable state. The rate at which a particular unstable atom decays is considered random and cannot be predicted precisely for just one atom. However, for a large number of atoms, a predictable average decay rate can be determined. This rate is often expressed in terms of half-life, which is the time it takes for half of the unstable atoms in a sample to decay.

The study of nuclear decay is critical for understanding the age of the earth and universe, nuclear energy generation, medical imaging, and various other aspects of physics, geology, and medicine.

Number of undecayed particles in the sample as a function of time elapsed Formula and Calculation

N(t) = N₀ ∙ e^{- ln 2/T_1/2 ∙ t}

This formula derived from

N(t) = N₀ e^{-λ ∙ t}

where

λ = ln 2/T_1/2

Nucleus Physics Physics Tutorials associated with the Nuclear Decay Calculator

The following Physics tutorials are provided within the Nucleus Physics section of our Free Physics Tutorials. Each Nucleus Physics tutorial includes detailed Nucleus Physics formula and example of how to calculate and resolve specific Nucleus Physics questions and problems. At the end of each Nucleus Physics tutorial you will find Nucleus Physics revision questions with a hidden answer that reveals when clicked. This allows you to learn about Nucleus Physics and test your knowledge of Physics by answering the test questions on Nucleus Physics.

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