Alpha Wolfram Calculator

Alpha Particle Kinetic Energy Calculator

Use this calculator to determine the kinetic energy of an alpha particle emitted during radioactive decay, based on the masses of the parent nucleus, daughter nucleus, and the alpha particle itself. This calculation is fundamental in nuclear physics to understand the energy released in alpha decay processes.

function calculateAlphaEnergy() { var parentMass = parseFloat(document.getElementById('parentMass').value); var daughterMass = parseFloat(document.getElementById('daughterMass').value); var alphaMass = parseFloat(document.getElementById('alphaMass').value); var resultDiv = document.getElementById('result'); resultDiv.innerHTML = "; // Clear previous results if (isNaN(parentMass) || isNaN(daughterMass) || isNaN(alphaMass) || parentMass <= 0 || daughterMass <= 0 || alphaMass <= 0) { resultDiv.innerHTML = 'Please enter valid positive numbers for all mass inputs.'; return; } // Constants var amuToMeV = 931.494; // Conversion factor: 1 amu = 931.494 MeV/c^2 // 1. Calculate Mass Defect (Δm) var massDefect = parentMass – daughterMass – alphaMass; // 2. Calculate Q-value (Energy released) var qValue = massDefect * amuToMeV; // 3. Calculate Alpha Particle Kinetic Energy // K_alpha = Q * (M_daughter / (M_daughter + M_alpha)) var alphaKineticEnergy = qValue * (daughterMass / (daughterMass + alphaMass)); resultDiv.innerHTML += 'Mass Defect (Δm): ' + massDefect.toFixed(6) + ' amu'; resultDiv.innerHTML += 'Q-value (Total Energy Released): ' + qValue.toFixed(4) + ' MeV'; resultDiv.innerHTML += 'Alpha Particle Kinetic Energy (K_α): ' + alphaKineticEnergy.toFixed(4) + ' MeV'; if (qValue <= 0) { resultDiv.innerHTML += 'Note: A non-positive Q-value indicates that the decay is not energetically favorable or cannot occur spontaneously.'; } } .alpha-wolfram-calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; border: 1px solid #ddd; border-radius: 8px; padding: 25px; max-width: 700px; margin: 20px auto; box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08); color: #333; } .alpha-wolfram-calculator-container h2 { color: #2c3e50; text-align: center; margin-bottom: 20px; font-size: 1.8em; } .alpha-wolfram-calculator-container p { line-height: 1.6; margin-bottom: 15px; } .calculator-form .form-group { margin-bottom: 18px; } .calculator-form label { display: block; margin-bottom: 8px; font-weight: bold; color: #555; } .calculator-form input[type="number"] { width: calc(100% – 22px); padding: 12px; border: 1px solid #ccc; border-radius: 5px; font-size: 1em; box-sizing: border-box; transition: border-color 0.3s ease; } .calculator-form input[type="number"]:focus { border-color: #007bff; outline: none; box-shadow: 0 0 0 3px rgba(0, 123, 255, 0.25); } .calculator-form button { background-color: #007bff; color: white; padding: 12px 25px; border: none; border-radius: 5px; cursor: pointer; font-size: 1.1em; display: block; width: 100%; margin-top: 25px; transition: background-color 0.3s ease, transform 0.2s ease; } .calculator-form button:hover { background-color: #0056b3; transform: translateY(-2px); } .calculator-result { background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 8px; padding: 20px; margin-top: 30px; } .calculator-result h3 { color: #28a745; margin-top: 0; margin-bottom: 15px; font-size: 1.5em; text-align: center; } .calculator-result p { margin-bottom: 10px; font-size: 1.1em; color: #333; } .calculator-result p strong { color: #0056b3; }

Understanding Alpha Decay and Kinetic Energy

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (a helium-4 nucleus, consisting of two protons and two neutrons) and transforms into a different atomic nucleus, known as the daughter nucleus. This process reduces the atomic number of the parent nucleus by 2 and its mass number by 4.

The Role of Mass Defect and Q-value

The energy released during alpha decay originates from a phenomenon called the mass defect. According to Einstein's famous equation, E=mc², a small amount of mass is converted into energy. In alpha decay, the total mass of the parent nucleus is slightly greater than the combined mass of the daughter nucleus and the alpha particle. This difference in mass is the mass defect (Δm).

The energy equivalent of this mass defect is known as the Q-value of the reaction. A positive Q-value indicates that the decay is energetically favorable and can occur spontaneously. The Q-value represents the total energy released during the decay, which is shared as kinetic energy between the emitted alpha particle and the recoiling daughter nucleus.

Kinetic Energy Distribution

Because momentum must be conserved in the decay process, the Q-value (total kinetic energy) is distributed between the alpha particle and the daughter nucleus. The lighter particle (the alpha particle) carries away a larger fraction of the kinetic energy, while the heavier daughter nucleus recoils with a smaller kinetic energy. The formula used in this calculator to determine the alpha particle's kinetic energy is derived from conservation of energy and momentum:

Kα = Q × (Mdaughter / (Mdaughter + Mα))

Where:

• Kα is the kinetic energy of the alpha particle.
• Q is the total energy released (Q-value).
• Mdaughter is the mass of the daughter nucleus.
• Mα is the mass of the alpha particle.

This equation shows that the alpha particle's kinetic energy is directly proportional to the Q-value and inversely proportional to the sum of the daughter and alpha particle masses, weighted by the daughter's mass.

Example: Radium-226 Decay

Let's consider the alpha decay of Radium-226 (²²⁶Ra) into Radon-222 (²²²Rn):

• Parent Nucleus Mass (²²⁶Ra): 226.025402 amu
• Daughter Nucleus Mass (²²²Rn): 222.017577 amu
• Alpha Particle Mass (⁴He): 4.002603 amu

Using the calculator with these values:

1. Mass Defect (Δm): 226.025402 – 222.017577 – 4.002603 = 0.005222 amu
2. Q-value: 0.005222 amu × 931.494 MeV/amu ≈ 4.864 MeV
3. Alpha Particle Kinetic Energy: 4.864 MeV × (222.017577 / (222.017577 + 4.002603)) ≈ 4.784 MeV

This means that when Radium-226 decays, the emitted alpha particle will typically have a kinetic energy of approximately 4.784 MeV, with the remaining energy going to the recoiling Radon-222 nucleus.