Analyze gamma decay with energy, wavelength, and time. Get equations, activity, remaining nuclei, and exports. Simple layout keeps every step readable on every screen.
| Case | Mode | Input | Key Output 1 | Key Output 2 | Key Output 3 |
|---|---|---|---|---|---|
| 1 | Energy gap | Ei = 1.25 MeV, Ef = 0 MeV | ν = 3.022487e+20 Hz | λ = 9.918736e-13 m | Eγ = 1.25 MeV |
| 2 | Wavelength | λ = 8.0e-13 m | ν = 3.747406e+20 Hz | Eγ = 1.549802 MeV | Photon relation used |
| 3 | Frequency | ν = 2.5e20 Hz | λ = 1.199170e-12 m | Eγ = 1.033917 MeV | Mass equivalent available |
| 4 | Time decay | N0 = 1.0e6, t1/2 = 6 h, t = 18 h | N(t) = 125000 | Remaining fraction = 0.125 | Three half-lives passed |
Energy difference: Eγ = Ei − Ef
Photon energy from frequency: E = hν
Photon energy from wavelength: E = hc / λ
Equivalent mass relation: E = Δmc2
Decay constant: λ = ln(2) / t1/2
Remaining quantity: N(t) = N0e−λt
Decay rate: A(t) = λN(t)
Expected gamma emissions: emissions = decayed quantity × branching ratio
Choose the calculation mode first.
Enter nuclide details if you want a specific gamma equation.
Fill only the fields related to your chosen mode.
Use energy levels for direct transition calculations.
Use wavelength or frequency when photon data is known.
Use mass defect to convert nuclear mass loss into gamma energy.
Use half-life mode for remaining quantity and emission estimates.
Press calculate to display the result above the form.
Download the result as CSV or save the page as PDF.
Gamma decay happens when an excited nucleus releases excess energy. The nucleus moves to a lower energy state. A gamma photon carries that energy away. The mass number stays the same. The atomic number also stays the same. That makes gamma decay different from alpha and beta decay.
The most common gamma decay relation is the energy balance. The photon energy equals the difference between two nuclear energy levels. That is Eγ = Ei − Ef. The same photon energy can also be written as E = hν and E = hc/λ. These linked equations let you solve energy, frequency, wavelength, and equivalent mass defect from one known value.
This calculator helps students, teachers, and analysts work faster. You can solve problems from several directions. Start with energy levels. Start with wavelength. Start with frequency. You can also estimate remaining nuclei over time from half-life. That makes the page useful for both nuclear equation practice and radioactive decay math.
A correct gamma decay equation shows the same nuclide on both sides. Only the energy state changes. The emitted symbol is γ. If the parent nucleus is marked with an excited state symbol, the daughter nucleus is the same isotope in a lower state. The output also converts values into joules, electron volts, megaelectron volts, hertz, and meters for easier comparison.
Some problems ask for the number of excited nuclei that remain after a given time. For that step, the calculator uses exponential decay. The main relation is N(t) = N0e−λt. The decay constant comes from λ = ln(2) / t1/2. Once λ is known, you can find the remaining quantity, decayed quantity, current activity, and expected gamma emissions.
Unit conversion is a common source of mistakes. This tool reduces that risk. It keeps the workflow clear and organized. It also shows an example table, export options, and a plain result block. That structure makes revision easier. It also supports homework checking, lab preparation, and quick concept review for nuclear physics and mathematical decay modeling.
Gamma decay is the release of excess nuclear energy as a gamma photon. The nucleus changes energy state, but the element itself stays the same.
No. Gamma emission does not change the atomic number or mass number. It only lowers the nucleus from an excited state to a lower state.
It uses Eγ = Ei − Ef, E = hν, E = hc/λ, E = Δmc², λ = ln(2)/t1/2, and N(t) = N0e−λt.
Yes. Enter the wavelength and choose the correct unit. The calculator converts it to meters, then finds frequency and photon energy automatically.
Many gamma problems involve how the emitting population changes over time. Half-life lets you estimate remaining nuclei, decay rate, and expected emissions.
The output can include joules, MeV, hertz, meters, picometers, atomic mass units, and per-second decay rates. That helps with classwork and cross-checking.
Branching ratio is the fraction of decays that produce the gamma path you are studying. A value of 100% means every decay follows that path.
Use the CSV button to download table data. Use the PDF button to open the print dialog and save the page as a PDF file.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.