Alpha Decay Equation Calculator

Formula Used

Nuclear equation: ^A_ZX → ^A-4_Z-2Y + ⁴₂He

Decay constant: λ = ln(2) / T_1/2

Remaining atoms: N(t) = N₀e^-λt

Decayed atoms: N_decayed = N₀ - N(t)

Activity: A(t) = λN(t), or A(t) = A₀e^-λt

Q value: Q = [m_parent - m_daughter - m_alpha] × 931.494 MeV

Energy sharing: E_alpha ≈ Q × m_daughter / (m_daughter + m_alpha)

How to Use This Calculator

1. Enter the parent element symbol, mass number, and atomic number.
2. Add the initial number of atoms in the sample.
3. Enter the half life and select its time unit.
4. Enter elapsed time to estimate remaining and decayed atoms.
5. Add activity if you want a separate activity decay check.
6. Add atomic masses if you need Q value and energy sharing.
7. Press the calculate button and review the result above the form.
8. Use the CSV or PDF button to save the result.

Example Data Table

Alpha Decay Equation Calculator Guide

Alpha decay is a nuclear change. A heavy parent nucleus emits one alpha particle. The alpha particle contains two protons and two neutrons. The parent therefore loses four mass units. Its atomic number also falls by two. This calculator turns that rule into a practical worksheet.

What the calculator solves

The tool balances the daughter nucleus from the parent mass number and atomic number. It also estimates decay constant, remaining atoms, decayed atoms, daughter atoms, and activity. You can enter a half life, an elapsed time, and an initial sample amount. You can also add atomic masses to estimate the Q value in mega electron volts.

Why alpha equations matter

Alpha equations help students check nuclear conservation. The total mass number must stay equal on both sides. The total atomic number must also stay equal. This makes the equation easy to verify. For example, uranium with mass number 238 and atomic number 92 becomes thorium with mass number 234 and atomic number 90.

Decay constant and activity

The decay constant describes the probability of decay per unit time. It comes from the half life. A larger constant means faster decay. Activity measures decays per second. It is reported in becquerels. When time passes, the undecayed atoms fall exponentially. The activity falls in the same way, when the half life remains constant.

Energy estimate

The Q value estimates released energy from a mass difference. Enter masses in atomic mass units. A positive Q value means the reaction can release energy. The calculator also estimates how that energy is shared between the alpha particle and the recoil daughter. These values are approximations. Real nuclear data may need exact isotope masses and excited state corrections.

Best use

Use this calculator for homework checks, lesson examples, and quick nuclear math. Enter realistic values. Choose matching time units. Review every step before copying results. The table helps compare sample cases. The export buttons let you save calculations for reports or classroom notes.

For advanced checks, compare atom based activity with entered activity. Differences may reveal rounded half life data, wrong units, or an impossible sample size. Treat every output as an estimate unless laboratory data confirms the isotope values fully.

FAQs