Mathematics · Quantum Mathematics
Hydrogen Energy Transition Calculator
Calculate hydrogen energy levels and the photon energy and wavelength between two principal quantum numbers.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Initial energy=−13.6÷3²=-1.511111111111111 eV; final energy=−13.6÷2²=-3.4 eV.
- Signed change=-3.4−(-1.511111111111111)=-1.8888888888888888 eV, so this is emission.
- Photon wavelength=hc/|ΔE|=6.563869328816484e-7 m=656.3869328816485 nm.
Problem → model → reason → result
What problem does this model solve?
Calculate hydrogen energy levels and the photon energy and wavelength between two principal quantum numbers.
Why does the model apply?
Hydrogen's allowed bound-state energies are discrete, so transitions emit or absorb photons with exactly the energy difference between levels.
What assumptions does it make?
Values use the displayed units and constants, states follow the stated normalization convention, and each calculation uses the named ideal non-relativistic quantum model.
Formula
Eₙ=−13.6 eV/n²; |ΔE|=hc/λ
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
The n=3 to n=2 transition releases about 1.89 eV, corresponding to roughly 656 nm red light.
Common mistake
This simplified formula is for hydrogen; multi-electron atoms require a different model.
When does this model not apply?
These introductory ideal models do not replace a full Hamiltonian, boundary conditions, uncertainty analysis, relativistic treatment or experimental interpretation for a real quantum system.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Hydrogen transition do?
Calculate hydrogen energy levels and the photon energy and wavelength between two principal quantum numbers.
How does the Hydrogen transition work?
The calculator applies Eₙ=−13.6 eV/n²; |ΔE|=hc/λ. Hydrogen's allowed bound-state energies are discrete, so transitions emit or absorb photons with exactly the energy difference between levels.
What can I learn from the Hydrogen transition?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.