1. What Are Hydrogen Atom Energy Levels?

The Bohr model describes hydrogen atom energy levels as quantized states where electrons can orbit the nucleus. These levels are given by the formula Eₙ = -13.6/n² eV, where n is the principal quantum number.

2. How Does the Calculator Work?

The calculator uses the hydrogen energy level equation:

Where:

• \( E_n \) — Energy of the level (eV)
• \( n \) — Principal quantum number (integer ≥1)
• 13.6 — Rydberg energy for hydrogen (eV)

Explanation: The negative sign indicates bound states, with n=1 being the ground state (-13.6 eV). Higher n values correspond to excited states with less negative (higher) energy.

3. Importance of Energy Level Calculation

Details: Understanding hydrogen energy levels is fundamental to atomic physics, explaining spectral lines and quantum transitions. The model serves as a foundation for more complex quantum mechanical treatments.

4. Using the Calculator

Tips: Enter any positive integer for n (1, 2, 3,...). The ground state is n=1 with energy -13.6 eV. Higher n values give energies closer to zero (ionization limit).

5. Frequently Asked Questions (FAQ)

Q1: Why is the energy negative?
A: Negative energy indicates the electron is bound to the nucleus. Zero energy would mean the electron is free (ionized).

Q2: What is the physical meaning of n?
A: The principal quantum number determines the electron's energy level and orbital size (n=1 is smallest).

Q3: How accurate is this formula?
A: It's exact for a non-relativistic hydrogen atom, but real atoms have small corrections from relativity and other effects.

Q4: Can this be used for other elements?
A: No, this simple formula only works for hydrogen or hydrogen-like ions with one electron.

Q5: What about energy differences between levels?
A: Transition energies can be calculated as ΔE = 13.6(1/n₁² - 1/n₂²) eV, which corresponds to emitted/absorbed photon energies.