1. What Is The Potential Energy Formula For An Electron?

The potential energy of an electron in an electric field is calculated using Coulomb's law. The formula represents the electrostatic potential energy between two point charges, where one charge is typically an electron.

2. How Does The Calculator Work?

The calculator uses the potential energy formula:

Where:

• \( PE \) — Potential energy (Joules)
• \( k \) — Coulomb's constant (8.99 × 10⁹ N m²/C²)
• \( e \) — Elementary charge (1.602 × 10⁻¹⁹ C)
• \( r \) — Distance between charges (meters)

Explanation: The negative sign indicates that the potential energy is attractive (bound state) for opposite charges.

3. Importance Of Potential Energy Calculation

Details: Calculating the potential energy of electrons is crucial in atomic physics, quantum mechanics, and understanding chemical bonding and atomic structure.

4. Using The Calculator

Tips: Enter Coulomb's constant in N m²/C², elementary charge in Coulombs, and distance in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the potential energy negative?
A: The negative sign indicates an attractive force between opposite charges, representing a bound state where energy is required to separate the charges.

Q2: What are typical values for these parameters?
A: Coulomb's constant is approximately 9×10⁹ N m²/C², elementary charge is 1.6×10⁻¹⁹ C, and atomic distances are typically on the order of 10⁻¹⁰ to 10⁻¹¹ meters.

Q3: Can this formula be used for other charged particles?
A: Yes, the formula applies to any two point charges by replacing e² with q₁q₂, where q₁ and q₂ are the respective charges.

Q4: How does distance affect potential energy?
A: Potential energy is inversely proportional to distance - as distance increases, the magnitude of potential energy decreases.

Q5: What are the units of potential energy?
A: Potential energy is measured in Joules (J) in the SI system, though electronvolts (eV) are commonly used in atomic and particle physics.