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Energy Transition Gap and Photon Frequency

Convert an energy-level gap to photon frequency, or recover either signed energy level, using exact Planck conversion and independent energy units.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 1 eV energy gap corresponds to approximately 241.799 THz. For example, levels at −3 eV and −4 eV differ by 1 eV.

ΔE = E_high − E_low; ν = ΔE/h; h = 6.62607015 ×10⁻³⁴ J·s.

Worked example

Enter these known values and leave the other values blank.

Higher-state energy
-3 eV
Lower-state energy
-4 eV
Transition energy gap
1 eV
Photon frequency
241.8 THz

Assumptions and limitations

  • Absolute energy levels may be negative, as for bound states referenced to a chosen zero. The higher level must have energy at least as large as the lower level. The transition gap is the nonnegative difference.
  • A downward transition can release the gap as a photon; absorption of the same energy can drive the reverse transition. This model assumes the supplied gap is carried by one photon and does not predict selection rules, transition probability, linewidth or recoil corrections.
  • The captured source supplies two level energies, their gap and photon frequency. It does not calculate Bohr orbits, principal quantum numbers, atomic number, a Rydberg spectrum or the levels themselves. Enter externally determined level energies.
  • Planck’s constant is the exact SI value 6.62607015 ×10⁻³⁴ J·s. One electronvolt is exactly 1.602176634 ×10⁻¹⁹ J. Hertz means cycles per second, not radians per second.
  • The retained RPM frequency choice expresses cycles per minute through division by 60. It does not assert rotation of an atom or photon. Watt-hours are energy, not power; 1 Wh = 3,600 J. Kilocalories use the thermochemical 4,184 J convention.
  • Equal levels give zero gap and zero frequency as an algebraic limit. That limit is not a physical emitted photon. Negative gap or frequency is rejected; negative absolute levels remain valid.
  • All four controls remain editable with locks. A gap or frequency determines the other, but neither alone determines the two absolute levels. Supply one level plus the gap or frequency to recover the other. Changing units preserves physical quantities.

Common questions

Can I enter negative energy levels?

Yes. Bound-state energies often use a negative reference. For example, −3 eV is higher than −4 eV, giving a positive 1 eV gap.

Does this calculate Bohr energy levels from quantum numbers?

No. It converts supplied energy levels into their gap and corresponding photon frequency. Quantum-number and atomic models are separate calculations.

Does frequency determine both levels?

No. It fixes their separation. Many pairs have the same gap; enter either absolute level to determine the other.

Is a zero-frequency result a real photon?

No. It is the equal-level, zero-energy limit of the arithmetic relationship. A real emitted photon has positive energy and frequency.

References

Use the exact SI Planck constant h = 6.62607015 ×10⁻³⁴ J·s in both photon-frequency directions, replacing the captured rounded value. Preserve the signed energy-level difference and all five inverse branches. Keep signed absolute energy levels while requiring ordered levels and nonnegative transition gap and frequency. Equal levels retain the zero-gap, zero-frequency algebraic limit, which is not emission of a physical photon.

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