Calculate Electron Energy in N 1

What is Electron Energy?

Electron energy in quantum mechanics describes the energy levels of electrons in atoms. The energy of an electron is quantized, meaning it can only take specific discrete values. For a hydrogen atom, the energy levels are determined by the principal quantum number n, which represents the electron's distance from the nucleus.

The ground state (n=1) is the lowest energy state of the electron in a hydrogen atom. Calculating the electron energy for n=1 provides fundamental information about the atom's stability and behavior.

Formula

The energy of an electron in a hydrogen atom can be calculated using the Rydberg formula:

Where:

• E = Energy of the electron (in joules)
• R∞ = Rydberg constant (1.0973731568539(55) × 10⁷ m⁻¹)
• h = Planck's constant (6.62607015 × 10⁻³⁴ J·s)
• c = Speed of light (299792458 m/s)
• n = Principal quantum number (for n=1)

For n=1, the formula simplifies to:

This represents the ground state energy of the electron in a hydrogen atom.

How to Use This Calculator

1. Enter the principal quantum number n (default is 1 for ground state).
2. Select the desired output unit (electron volts, joules, or kilojoules).
3. Click "Calculate" to compute the electron energy.
4. Review the result and use the chart to visualize the energy levels.

Example Calculation

Let's calculate the electron energy for n=1:

This means the electron in the ground state has an energy of -13.6 electron volts. The negative sign indicates that the electron is bound to the nucleus.