Solve atomic hyperfine level shifts from quantum numbers. Estimate intervals, frequencies, wavelengths, and energies instantly. Built for spectroscopy checks, teaching notes, and lab planning.
| Example | I | J | F1 | F2 | A (MHz) | B (MHz) | Gap (MHz) | Wavelength (m) |
|---|---|---|---|---|---|---|---|---|
| Sample 1 | 0.5 | 0.5 | 1 | 0 | 1420.405751 | 0 | 1420.405751 | 0.211061 |
| Sample 2 | 1.5 | 1.5 | 3 | 2 | 120 | 25 | 385 | 0.778682 |
| Sample 3 | 1.5 | 0.5 | 2 | 1 | 250 | 0 | 500 | 0.599585 |
The calculator uses the standard hyperfine structure energy expression:
E(F) = (A/2)K + B × [((3/4)K(K+1) - I(I+1)J(J+1)) / (2I(2I-1)J(2J-1))]
K = F(F+1) - I(I+1) - J(J+1)
A is the magnetic dipole constant. B is the electric quadrupole constant. I is nuclear spin. J is electronic angular momentum. F is total angular momentum. The transition frequency is found from the absolute energy difference divided by Planck's constant. The wavelength is then c divided by that frequency.
A hyperfine splitting calculator helps you estimate small energy differences inside atomic or molecular levels. These differences come from the interaction between the nucleus and the electron cloud. The tool is useful in spectroscopy, atomic physics, laser experiments, and frequency standard studies.
Hyperfine structure changes the exact position of spectral lines. Even tiny shifts can affect precision work. Researchers use these values when studying transition frequencies, level intervals, microwave radiation, and wavelength changes. Students also use them to check quantum number relationships and selection rule examples.
This calculator uses nuclear spin I, electronic angular momentum J, and total angular momentum F. It also uses the magnetic dipole constant A and the electric quadrupole constant B. With these inputs, the page computes the K term, individual energy shifts, total splitting, transition frequency, and wavelength.
The result section gives more than one final number. It breaks the answer into dipole and quadrupole terms for each level. That makes it easier to inspect the contribution from each interaction. You can compare two F states, inspect the signed gap, and export the summary for reports, lab notes, or class material.
The quadrupole term only works when the denominator in the B expression is defined. If I or J is too small, the B contribution does not apply. In those cases, the calculator keeps the model stable and uses the dipole term only. This helps prevent invalid results and supports quick checking.
Frequency output is useful when you compare predicted lines with microwave or radio measurements. Wavelength output helps when you want a quick scale conversion, even though many hyperfine transitions sit outside visible light. Because the calculator reports both level shifts and the transition gap, you can inspect the physics from two angles. This is useful for lecture examples, data screening, and preparing input values before a more detailed quantum model.
This page fits students, teachers, and researchers who need a fast hyperfine structure reference. It is helpful for spectroscopy homework, microwave transition checks, isotope comparisons, and atomic line analysis. The simple layout keeps the workflow clean, while the advanced formula support keeps the physics practical and reliable.
Hyperfine splitting is the small separation of atomic or molecular energy levels caused by interactions between nuclear moments and electronic angular momentum.
The A constant measures the magnetic dipole interaction strength. It often dominates the splitting when the quadrupole term is absent or negligible.
Use B when the electric quadrupole interaction is relevant and the denominator in the quadrupole formula is defined. Otherwise, set B to zero.
Quantum angular momenta can be integers or half-integers. That is why the calculator accepts steps of 0.5 for I, J, and F.
F must lie between |I − J| and I + J. If your value falls outside that range, the state is not physically allowed.
Use the unit that matches your source data. The calculator converts frequency or energy units internally before producing the final results.
It represents the wavelength associated with the absolute transition frequency between the two selected hyperfine states.
Yes. After calculation, use the CSV or PDF buttons to save the result table for reports, lab records, or study notes.
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.