The eV to Velocity Calculator determines the velocity of a particle given its kinetic energy in electronvolts (eV). This tool is essential in fields such as particle physics, plasma science, and materials research where particles like electrons, protons, or ions are accelerated and their velocities must be calculated precisely.
Because electronvolts represent energy and not speed, the calculator converts energy to joules, then uses the classical kinetic energy formula to determine the corresponding velocity. This bridges the gap between energy measurements and dynamic behavior of particles, especially in vacuum systems, beam dynamics, and semiconductor devices.
Formula of eV to Velocity Calculator
Where:
- v = velocity in meters per second (m/s)
- E = energy in electronvolts (eV)
- q = 1.602176634 × 10⁻¹⁹ C (elementary charge to convert eV to joules)
- m = mass of the particle in kilograms
Step-by-step breakdown:
- Convert energy from eV to joules:
E_J = E × q - Use the kinetic energy formula to calculate velocity:
v = √[(2 × E_J) / m]
This method assumes non-relativistic speeds and is valid as long as the velocity remains well below the speed of light.
Helpful Reference Table
Here’s a reference table showing approximate velocities for different energies (for an electron with mass ≈ 9.10938356 × 10⁻³¹ kg):
| Energy (eV) | Velocity (m/s) |
|---|---|
| 1 | 593,100 |
| 10 | 1,875,700 |
| 50 | 4,190,200 |
| 100 | 5,931,000 |
| 500 | 1.326 × 10⁷ |
| 1000 | 1.875 × 10⁷ |
These values offer a quick lookup to estimate particle speeds in experiments or simulations.
Example of eV to Velocity Calculator
Let’s calculate the velocity of an electron with a kinetic energy of 10 eV.
Step 1: Convert energy to joules
E_J = 10 × 1.602176634 × 10⁻¹⁹ = 1.602176634 × 10⁻¹⁸ J
Step 2: Use the kinetic energy formula
v = √[(2 × 1.602176634 × 10⁻¹⁸) / (9.10938356 × 10⁻³¹)]
v ≈ √(3.518 × 10¹²) ≈ 1,875,700 m/s
Result: The velocity of an electron with 10 eV of energy is approximately 1.88 million meters per second.
Most Common FAQs
You can use it for any particle, as long as you provide the correct mass in kilograms. Common examples include electrons, protons, neutrons, or ions.
The formula is accurate only for non-relativistic cases. If the velocity approaches a significant fraction of the speed of light, relativistic corrections using Einstein’s theory of relativity are necessary.
eV is a convenient unit in atomic and particle physics because it naturally fits the energy scales involved in these systems. It simplifies many calculations, especially when dealing with single particles or atomic interactions.