Energy Level Diagram Calculator

Calculator Inputs

The page stays in a single main flow, while the calculator fields use a 3 column layout on large screens, 2 on medium, and 1 on mobile.

Atomic Number (Z)

Use 1 for H, 2 for He⁺, 3 for Li²⁺, and similar systems.

Calculation Mode

Choose automatic shielding or directly enter Z_eff.

Shielding Factor (S)

Auto mode uses Z_eff = Z - S.

Manual Effective Nuclear Charge

Used only when manual mode is selected.

Initial Principal Level (n_i)

Final Principal Level (n_f)

Levels To Display

The calculator automatically expands this if your transition needs more levels.

Decimal Precision

Highlighted Energy Unit

Show continuum line at 0 eV

Reset

Example Data Table

These sample rows show how hydrogen-like systems produce different transition energies and wavelengths.

System	Transition	Z_eff	\|ΔE\| (eV)	Wavelength (nm)	Type	Series
Z=1	3 → 2	1.0000	1.8889	656.3869	Emission	Balmer
Z=2	4 → 2	2.0000	10.2000	121.5531	Emission	Balmer
Z=3	5 → 3	3.0000	8.7040	142.4451	Emission	Paschen

Formula Used

1. Effective nuclear charge
Z_eff = Z - S (auto mode)
or use a direct manual Z_eff.

2. Energy of level n
E_n = -13.6 × Z_eff² / n² eV

3. Transition energy
ΔE = E_final - E_initial
Photon energy magnitude = |ΔE|

4. Wavelength and frequency
λ = h c / E_photon
ν = E_photon / h

5. Wavenumber and ionization from a level
ṽ = 1 / λ (in cm^-1)
Ionization energy from level n = |E_n|

How To Use This Calculator

Enter the atomic number for your hydrogen-like atom or ion.
Choose auto mode for Z - S, or manual mode for direct Z_eff.
Set the initial and final principal quantum levels.
Choose how many levels should appear in the plotted diagram.
Select decimal precision and your preferred highlighted energy unit.
Click Calculate Diagram to show results above the form.
Review the chart, detailed outputs, and level energy table.
Use the CSV and PDF buttons to export your results.

FAQs

1. What does this calculator measure?

It estimates atomic energy levels, transition energy, wavelength, frequency, wavenumber, and ionization energy using a hydrogen-like approximation. It also plots the transition on an energy level diagram.

2. Which atoms or ions fit this model best?

The model is most accurate for one-electron systems such as hydrogen, He⁺, and Li²⁺. Shielding-based estimates can still be useful for simplified comparisons in other atoms.

3. Why are the level energies negative?

Negative energy means the electron is bound to the nucleus. Zero energy represents the continuum limit, where the electron is free and fully ionized.

4. How does the calculator decide emission or absorption?

If the initial level is higher than the final level, the transition is emission. If the final level is higher, the atom must absorb energy, so the transition is absorption.

5. What is the role of effective nuclear charge?

Effective nuclear charge reflects how strongly the nucleus attracts the electron after accounting for shielding. A larger Z_eff makes levels more negative and raises transition energies.

6. What does the series family mean?

The series labels group transitions by the lower reference level. Common families include Lyman, Balmer, Paschen, Brackett, Pfund, and Humphreys.

7. Why might the wavelength fall outside visible light?

Many atomic transitions produce ultraviolet or infrared photons. Visible light is only a narrow band, roughly 380 to 750 nm, so many valid transitions fall beyond it.

8. Can I export my results for reports or class notes?

Yes. The calculator includes CSV export for tabular data and PDF export for a formatted snapshot of the result area, including the plot and summary tables.