Quantized Energy Levels Simulator — Hydrogen Energy Ladder & Transition Wavelengths Interactive

Interactive 3D hydrogen energy-level ladder: choose upper and lower principal levels, switch between emission and absorption, and read the transition energy, photon wavelength and frequency on a spectrum ruler.

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About the Quantized Energy Levels Simulator

Explore hydrogen level energies using a vertical energy ladder, a pulsed transition indicator and a photon wave train. Emission releases the level difference; absorption requires that same energy.

What the simulator shows

• A hydrogen energy ladder, an occupied-state marker, a photon wave train, a wavelength reference ruler and a transition-energy guide. • Controls for the upper principal level n, the lower principal level n, transition direction and demonstration playback speed. • Four tabs: Observatory, Geometry & measurements, Experiments (with built-in model checks), and Learn & assess.

The mathematics

En = −13.6/n² eV (reduced-mass and fine-structure corrections omitted). ΔE = Eupper − Elower and λ = 1239.841984/ΔE nm; f = ΔE/(4.135667696×10⁻¹⁵) Hz. Emission is upper → lower + photon; absorption is lower + photon → upper.

Model boundaries

This is an ideal energy-difference model using principal n levels only: selection rules, degeneracy, line widths, transition probabilities, cascades and lifetimes are not resolved. The 4-second demonstration cycle re-prepares the atom and is not a radiative lifetime. For an invalid upper ≤ lower choice, photon readouts show zero and animation is disabled.

Frequently asked questions

Does emission release the difference in level energies?

Yes. Conservation of energy sets the photon energy to Eupper − Elower.

Is the four-second cycle a real atomic lifetime?

No. It is a slowed teaching cycle that includes re-preparing the atom.

What wavelength does the n=3 to n=2 transition give?

The hydrogen n=3→2 energy difference gives about 656.4 nm (Balmer H-alpha), while n=2→1 gives about 121.6 nm, outside visible light.

What does absorption require?

The incoming photon transfers the same positive energy required for the reverse emission transition: lower level + photon → upper level.

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