Enter Ion and Level Data
Formula Used
The calculator uses the Bohr energy expression for a one-electron ion. For Li2+, the nuclear charge is three, so the ideal ground-state energy is nine times the hydrogen ground-state ionization energy.
E = R∞ × (μ / me) × Zeff2 / (n - δ)2
λ = hc / E and f = E / h
Here, E is ionization energy. R∞ is 13.605693122994 eV. Zeff is effective charge. n is the principal level. δ is quantum defect. μ / me is the reduced mass factor.
How to Use This Calculator
Select the Li2+ model for the common physics problem. Enter n = 1 for the ground state. Keep quantum defect at zero for an ideal hydrogen-like ion. Enable reduced mass if you need a higher precision value. Add a photon wavelength to test whether light can ionize the ion.
Press Calculate to view energy in eV, joules, kJ/mol, wavelength, frequency, and temperature. Use CSV or PDF buttons when you need a saved result for notes, reports, or laboratory records.
Example Data Table
| Ion or model | Z or Zeff | n | Energy estimate | Threshold wavelength |
|---|---|---|---|---|
| Hydrogen | 1 | 1 | 13.6057 eV | 91.18 nm |
| He+ | 2 | 1 | 54.4228 eV | 22.80 nm |
| Li2+ | 3 | 1 | 122.4512 eV | 10.13 nm |
| Li2+ excited | 3 | 2 | 30.6128 eV | 40.50 nm |
Understanding Li2+ Ionization Energy
Li2+ is a lithium nucleus with only one bound electron. That makes it hydrogen-like. The electron feels a strong nuclear charge. The Bohr model works well because electron shielding is absent. The main input is the nuclear charge, which is Z = 3 for lithium.
Ionization energy is the energy required to remove the electron completely. The reference point is an electron at infinite distance. For the ground state, the energy scales with Z squared. Hydrogen has 13.6057 eV in the first level. Li2+ has nine times that value, before small mass corrections.
Role of Quantum Level
The principal quantum number controls the binding strength. A larger n places the electron farther from the nucleus. The energy then drops with n squared. The n = 2 level of Li2+ needs only one fourth of the ground state energy. This is why excited ions ionize more easily.
The calculator also includes a quantum defect option. For a pure one-electron Coulomb field, this value is zero. A nonzero value can be useful for approximate comparisons with screened atoms or fitted spectral data.
Reduced Mass and Precision
Simple classroom work often assumes an infinite nuclear mass. Real nuclei move slightly around the shared center of mass. The reduced mass correction accounts for this effect. It changes the result by a small amount. The correction matters when spectra are compared with precise measurements.
Photon Threshold
Ionization can happen when a photon carries at least the binding energy. The calculator converts energy to a threshold wavelength using hc divided by E. Shorter wavelengths have higher energy. For ground-state Li2+, the threshold lies in the extreme ultraviolet region.
If a photon wavelength is entered, the tool compares photon energy with the threshold. It also reports excess energy. In a simple photoionization picture, excess energy becomes kinetic energy of the released electron. The speed estimate is nonrelativistic, so it is best for moderate excess values.
Using Results in Physics
These results help with atomic physics, spectroscopy, plasma modeling, and homework checks. Values in eV are best for single ions. Joules per ion are useful for dimensional analysis. Kilojoules per mole help connect atomic energy with chemical energy scales.
Common Mistakes
Do not use neutral lithium data for Li2+. Neutral lithium has shielding, so its first ionization energy is much smaller. Do not confuse Li+ with Li2+. Li+ still has two electrons. Li2+ has one electron. Also keep n positive. A negative effective level has no physical meaning. When using photons, remember that shorter wavelength means larger energy. Save input settings with every calculation for later review and grading carefully.
The Li2+ case is important because it shows the power of the hydrogen-like formula. It also shows why highly charged ions hold electrons tightly. Always match the model to the physical system. Use zero defect for Li2+. Use careful inputs, and always review your significant figures.
Frequently Asked Questions
What is Li2+?
Li2+ is a lithium ion with two electrons removed. It has a nucleus with charge +3e and one remaining electron, so it behaves like a hydrogen-like ion.
What is the ground-state ionization energy of Li2+?
The ideal Bohr value is about 122.451 eV when reduced mass is ignored. A reduced mass correction changes it slightly.
Why does the formula use Z squared?
The Coulomb attraction grows with nuclear charge. In the Bohr model, the binding energy of a one-electron ion scales as Z squared divided by n squared.
Should I set quantum defect to zero?
Yes, for ideal Li2+ calculations. Quantum defect is mainly useful for approximate screened atoms, fitted data, or non-ideal comparisons.
What does reduced mass correction do?
It accounts for slight nuclear motion. The electron and nucleus orbit their shared center of mass, so the binding energy is slightly adjusted.
Can this calculator handle other ions?
Yes. Choose the custom one-electron ion model and enter the nuclear charge Z. The formula works for hydrogen-like ions.
What is threshold wavelength?
It is the longest photon wavelength that can ionize the selected level. Longer wavelengths have less energy and cannot cross the threshold.
Why are kJ/mol values included?
They convert single-ion energy into a molar scale. This helps compare atomic physics values with chemical thermodynamics and reaction energies.
Does photon excess energy matter?
Yes. After ionization, excess photon energy can become kinetic energy of the freed electron in a simple photoelectric-style model.
Is this result exact for real experiments?
It is very good for a one-electron model. Very precise experiments may require additional corrections from relativistic effects and nuclear size.
Which unit should I use for homework?
Use eV for atomic calculations. Use joules when your formula needs SI units. Use kJ/mol when comparing with molar energy values.