Calculator
Example Data Table
| Field | State | mJ | gJ | Shift factor | Energy shift |
|---|---|---|---|---|---|
| 1 T | 2S1/2 | +1/2 | 2.0000 | 1.0000 | 5.78838E-5 eV |
| 1 T | 2P1/2 | +1/2 | 0.6667 | 0.3333 | 1.92946E-5 eV |
| 1 T | 2P3/2 | +3/2 | 1.3333 | 2.0000 | 1.15768E-4 eV |
Formula Used
The calculator uses first order weak field Zeeman relations.
- Landé factor: gJ = 1 + [J(J + 1) + S(S + 1) - L(L + 1)] / [2J(J + 1)]
- Anomalous shift: delta E = muB gJ mJ B
- Normal orbital shift: delta E = muB mL B
- Spin shift: delta E = muB ge mS B
- Frequency shift: delta nu = delta E / h
- Wavenumber shift: delta sigma = delta E / hc
- Transition offset: delta E line = delta E upper - delta E lower
- Small wavelength shift: delta lambda is about -lambda squared times delta nu divided by c
How to Use This Calculator
- Enter the magnetic field and choose its unit.
- Select the Landé, normal, or spin calculation model.
- Choose a preset n=2 state or enter custom values.
- Enter the matching magnetic quantum number.
- Add transition states when a spectral line offset is needed.
- Press calculate and review the result above the form.
- Use CSV or PDF download for records.
Article
What the calculator does
This calculator estimates weak field Zeeman splitting for the n=2 hydrogen atom. It focuses on magnetic shifts caused by an external field. You can study 2S and 2P states. You can also enter custom quantum numbers for controlled checks.
Why n=2 hydrogen is useful
Hydrogen is useful because its levels have clear quantum labels. For n=2, the allowed orbital values are l=0 and l=1. Spin adds fine structure labels through j. The Landé factor connects l, s, and j with the magnetic moment. When a field is applied, each allowed m value moves by a different amount.
Reading the results
The calculator uses the Bohr magneton to convert field strength into energy. It then reports the shift in electronvolts and joules. It also converts the same shift into frequency and wavenumber units. These outputs help compare spectroscopy notes, lab data, and textbook examples.
Model choices
The normal option uses only the orbital magnetic quantum number. It is helpful for simple triplet splitting. The anomalous option uses the Landé factor. It is better for hydrogen states with spin. A spin only option is included for quick magnetic moment checks.
Transition offsets
For transitions, the tool subtracts the lower state shift from the upper state shift. This gives the spectral line offset. The wavelength change is an approximation. It works best when the shift is small compared with the rest frequency. Selection guidance is also shown using the change in magnetic quantum number.
Practical notes
Results should be read as first order values. Very strong fields can need Paschen Back treatment. Fine structure, Lamb shift, and hyperfine terms are not fully modeled here. Use this page for learning, estimates, and reports. Use specialist software for precision atomic research.
Simple workflow
Start with a small field, such as one tesla. Choose a level preset. Enter a valid m value. Then compare positive and negative m values. The signs show which sublevels rise or fall. Export the table when you need to save or share the calculation.
Example support
The example table gives typical entries for common states. It helps users confirm units before using their own data. The calculator is not a replacement for careful derivation. It is a practical worksheet that keeps constants, signs, and conversions in one place for faster review. It supports classroom demonstrations and quick checks too.
FAQs
What does n=2 mean in hydrogen?
It is the second principal energy level. In hydrogen, n=2 includes 2S and 2P states. Those states split into magnetic sublevels when an external magnetic field is applied.
Which model should I choose?
Use the Landé model for hydrogen levels with spin. Use the normal model for a simple orbital view. Use the spin model for isolated spin magnetic moment checks.
What is mJ?
mJ is the magnetic quantum number for total angular momentum J. It runs from -J to +J in whole steps. Each allowed mJ value has a different shift.
Can this handle very strong fields?
It is intended for weak field calculations. Very strong fields may require Paschen Back analysis. Fine structure mixing can also matter in stronger fields.
Why are frequency and wavenumber shown?
Spectroscopy often uses frequency and wavenumber units. Showing both makes the result easier to compare with lab instruments, line tables, and course notes.
What rest wavelength should I enter?
Use the unshifted spectral line wavelength. For Lyman alpha, 121.567 nm is a common reference. You can enter another wavelength for a different line.
Are fine structure and Lamb shift included?
No. The calculator reports first order magnetic shifts. It does not fully model fine structure, Lamb shift, hyperfine splitting, or detailed radiative corrections.
What does the transition selection guide mean?
It checks the simple electric dipole rule for delta m. A delta of 0 gives a pi candidate. A delta of plus or minus 1 gives a sigma candidate.