1. What is the Hydrogen Atom Energy Equation?

The hydrogen atom energy equation calculates the energy of an electron in a hydrogen atom at a specific energy level (principal quantum number n). This fundamental quantum mechanical formula describes the discrete energy levels available to electrons in hydrogen atoms.

2. How Does the Calculator Work?

The calculator uses the hydrogen atom energy equation:

Where:

• \( E \) — Energy of the electron (eV)
• \( n \) — Principal quantum number (n = 1, 2, 3...)
• 13.6 — Rydberg constant for hydrogen (eV)

Explanation: The equation shows that energy levels in hydrogen atoms are quantized and inversely proportional to the square of the principal quantum number.

3. Importance of Energy Calculation

Details: Calculating hydrogen atom energy levels is fundamental to understanding atomic structure, spectral lines, quantum transitions, and the behavior of electrons in atoms.

4. Using the Calculator

Tips: Enter the principal quantum number (n) as a positive integer (n ≥ 1). The calculator will compute the corresponding energy level in electron volts (eV).

5. Frequently Asked Questions (FAQ)

Q1: What does the 13.6 eV represent?
A: 13.6 eV is the ionization energy of hydrogen - the energy required to remove an electron from the ground state (n=1) to infinity.

Q2: Why is the energy negative?
A: The energy is negative because it represents the binding energy of the electron to the nucleus. Zero energy corresponds to a free electron.

Q3: What are the allowed values for n?
A: n must be a positive integer (1, 2, 3, ...). Each value corresponds to a specific electron shell (K, L, M, etc.).

Q4: How does this relate to spectral lines?
A: The difference between energy levels determines the wavelength of photons emitted or absorbed during electron transitions.

Q5: Is this formula accurate for other atoms?
A: This exact formula applies only to hydrogen and hydrogen-like ions (single electron systems). Multi-electron atoms require more complex calculations.