Bohr's Equation Calculator

Bohr's Energy Equation:

\[ \Delta E = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Energy Difference (ΔE):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Bohr's Energy Equation?

Bohr's energy equation calculates the energy difference between two electron orbits in a hydrogen atom. It's a fundamental equation in quantum physics that describes electron transitions and the resulting photon emissions.

2. How Does the Calculator Work?

The calculator uses Bohr's energy equation:

\[ \Delta E = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Where:

\( \Delta E \) — Energy difference in electron volts (eV)
\( n_1 \) — Initial principal quantum number (energy level)
\( n_2 \) — Final principal quantum number (energy level)
13.6 — Rydberg energy for hydrogen (eV)

Explanation: The equation shows that energy is quantized in atoms, with electrons occupying specific energy levels. Transitions between levels result in absorption or emission of photons.

3. Importance of Energy Level Calculations

Details: Calculating energy differences helps predict the wavelengths of light emitted or absorbed during electron transitions, explaining atomic spectra and quantum behavior.

4. Using the Calculator

Tips: Enter integer values for both energy levels (n₁ and n₂). For emission spectra, n₂ < n₁; for absorption spectra, n₂ > n₁.

5. Frequently Asked Questions (FAQ)

Q1: Why does the equation use 13.6 eV?
A: 13.6 eV is the ionization energy of hydrogen - the energy needed to completely remove an electron from the ground state (n=1).

Q2: Does this work for other elements?
A: The equation is exact only for hydrogen-like atoms (single electron systems). For multi-electron atoms, modifications are needed.

Q3: What's the significance of the negative sign in results?
A: A negative ΔE indicates energy is emitted (photon released), while positive means energy is absorbed (photon absorbed).

Q4: How are energy levels related to spectral lines?
A: Each transition corresponds to a specific spectral line. The energy difference determines the photon's wavelength (E = hc/λ).

Q5: What are the limitations of Bohr's model?
A: It doesn't explain fine structure, Zeeman effect, or multi-electron atoms. Quantum mechanics provides more complete descriptions.