The Alpha Decay Calculator determines the daughter nucleus, Q-value (energy released), and alpha particle kinetic energy for any alpha-decaying isotope. Used in nuclear physics, radiochemistry, radiation protection, and nuclear medicine to characterize alpha-emitting radionuclides.
4.8717
MeV
4.7855
MeV
0.0862
MeV
0.05067
c
36,580,013,499.368
Bq/g
4.8717
MeV
4.7855
MeV
0.0862
MeV
0.05067
c
36,580,013,499.368
Bq/g
The calculator for alpha decay determines the daughter nucleus produced, the Q-value (total energy released), and the kinetic energy imparted to the alpha particle when a parent nucleus undergoes alpha emission. Alpha decay occurs predominantly in heavy nuclei above mass number 200, where the nuclear binding energy per nucleon decreases with increasing size.
In alpha decay, a parent nucleus emits an alpha particle (helium-4: 2 protons + 2 neutrons), producing a daughter with atomic number reduced by 2 and mass number reduced by 4:
ᴬ_Z → ᴬ⁻⁴_(Z-2) + ⁴_₂He
For example, uranium-238 alpha decays to thorium-234: ²³⁸U → ²³⁴Th + ⁴He. The daughter nucleus is always two elements lower in the periodic table. The decay conserves charge (proton number), baryon number (mass number), energy (Q-value), and momentum (determining energy distribution between products). The Q-value calculator provides the energy release calculation for any nuclear reaction.
The Q-value equals the mass-energy difference between parent and products: Q = (M_parent − M_daughter − M_alpha) × 931.5 MeV/u. By conservation of momentum, the alpha particle carries the larger fraction of this energy since it is much lighter than the daughter nucleus: T_alpha = Q × M_daughter / (M_alpha + M_daughter). For ²³⁸U: Q = 4.27 MeV and T_alpha = 4.27 × 234/(4 + 234) = 4.20 MeV — consistent with the measured value. Use this online calculator for any alpha-decaying isotope with known atomic masses.
A key feature of alpha decay is the extreme sensitivity of half-life to Q-value, described by the Geiger-Nuttall law: log(λ) = a − b/√Q. A small change in Q produces an enormous change in half-life through quantum mechanical tunneling through the Coulomb barrier. ²³⁸U (Q = 4.27 MeV) has a half-life of 4.47 × 10⁹ years; ²¹²Po (Q = 8.95 MeV) has a half-life of only 299 nanoseconds — the same ~5 MeV difference spans ~24 orders of magnitude in half-life. The nuclear binding energy calculator and nuclear physics calculators provide complementary nuclear energy tools.
Alpha particles are heavily ionizing but have very short range: typically 3–7 cm in air and less than 100 micrometers in tissue. External alpha exposure is generally harmless. However, internal alpha emitters are among the most radiobiologically dangerous sources of ionizing radiation. When inhaled or ingested, alpha emitters deposit their entire energy in a small volume of tissue with 20× the DNA-damaging effectiveness of gamma radiation per unit energy. Radon-222 is the second leading cause of lung cancer after smoking — a direct consequence of alpha particle emission in the lung epithelium.
Enter the atomic masses of the parent and daughter nuclei in atomic mass units (from AME tables), the parent mass number A, and the half-life in years. The calculator computes Q-value, kinetic energy distribution between alpha and daughter, alpha particle speed, and specific activity.
A positive Q-value confirms that alpha decay is energetically allowed. Alpha particles typically emerge with 4-9 MeV of kinetic energy at speeds of 5-10% of the speed of light. Higher Q-values generally correspond to shorter half-lives (Geiger-Nuttall law).
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Results
Ra-226 decays to Rn-222. The 4.785 MeV alpha matches experimental value. Specific activity 3.66 × 10^10 Bq/g defines 1 Curie (1 Ci = 3.7 × 10^10 Bq).
Inputs
Results
Po-210 half-life is 138.4 days (0.379 yr). High specific activity of 1.66 × 10^14 Bq/g explains its extreme radiotoxicity.
Alpha decay is energetically favored for nuclei with Z above about 52 (tellurium) because the nuclear binding energy per nucleon decreases for very heavy nuclei. The alpha particle has unusually high binding energy (28.3 MeV) making its emission energetically favorable. Lighter nuclei would require negative Q-values for alpha emission.
The Geiger-Nuttall law (1911) states that log(t½) is linearly related to 1/√Q_alpha for a given element. This means a small increase in Q-value leads to a dramatic decrease in half-life. For example, in the uranium decay series, U-238 (Q=4.27 MeV, t½=4.5 Gyr) versus Po-212 (Q=8.95 MeV, t½=0.3 μs).
Using classical kinetic energy (valid since v/c is typically less than 10%): KE = ½mv², so v = √(2KE/m). With KE in Joules (convert from MeV using 1 MeV = 1.602 × 10⁻¹³ J) and m = 4 × 1.661 × 10⁻²⁷ kg (alpha mass), we get the speed. Relativistic corrections are small but can be included for high-energy alphas.
Specific activity is the number of radioactive decays per second per gram of material. It is calculated as A = (ln2 × N_A) / (t½ × M), where N_A is Avogadro's number and M is molar mass. Short-lived isotopes have much higher specific activities than long-lived ones.
Alpha particles have a linear energy transfer (LET) of about 100 keV/μm, compared to about 0.2 keV/μm for gamma rays. This concentrated energy deposition causes severe DNA damage within the cell. The radiation weighting factor for alpha particles is 20, meaning 1 Gy of alpha radiation causes the same biological damage as 20 Gy of gamma radiation.
Many alpha decays produce alpha particles with discrete energies corresponding to transitions to different energy levels of the daughter nucleus. The most energetic alphas lead to the ground state. Less energetic alphas leave the daughter in an excited state, which then emits gamma rays. Measuring these spectra fingerprints the isotope precisely.
Targeted alpha therapy (TAT) uses alpha emitters conjugated to tumor-seeking molecules. Approved examples include Ra-223 dichloride (Xofigo) for bone metastases from prostate cancer, and Ac-225 / Bi-213 systems in clinical trials for leukemia and solid tumors. The short range (40-90 μm in tissue) limits collateral damage to healthy cells.
Nuclear theory predicts that nuclei with certain magic numbers of protons and neutrons (Z=114, N=184) may have significantly enhanced stability compared to neighboring nuclides — the 'island of stability.' Some superheavy elements like Fl-290 show half-lives of seconds rather than milliseconds, suggesting we are on the slopes of this island.
Yes — radioisotope thermoelectric generators (RTGs) use alpha-emitting isotopes (typically Pu-238, half-life 87.7 years, Q=5.59 MeV) to generate heat via alpha absorption, which is converted to electricity by thermocouples. RTGs power deep space probes like Voyager, Cassini, and the Mars Curiosity rover.
In soft tissue, alpha particles with 5-6 MeV (typical) have a range of 35-50 micrometers, roughly half the diameter of a cell nucleus to the width of a few cells. This can be calculated using the Bragg-Kleeman rule or NIST ASTAR tables. The Bragg peak at the end of the range is where maximum ionization occurs.
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