Particles Velocity Calculator

Calculation Method:

Kinetic Energy:

Particle Mass:

Particle Velocity (m/s): Particle Velocity (km/s): Particle Velocity (mph): Particle Velocity (% of c): Particle Velocity (Hz):

1. What is a Particles Velocity Calculator?

Definition: This calculator computes the velocity of particles (e.g., electrons, protons) using kinetic energy, momentum, or mass and acceleration, applying classical or relativistic physics based on speed.

Purpose: It is used in particle physics, quantum mechanics, and high-energy physics to determine particle speeds in accelerators, cosmic rays, or material interactions.

2. How Does the Calculator Work?

The calculator uses these formulas:

\[ v = \sqrt{\frac{2E_k}{m}} \quad \text{(Classical, Kinetic Energy)} \] \[ v = c \sqrt{1 - \left(\frac{mc^2}{E_k + mc^2}\right)^2} \quad \text{(Relativistic, Kinetic Energy)} \] \[ v = \frac{p}{m} \quad \text{(Classical, Momentum)} \] \[ v = \frac{pc}{\sqrt{(pc)^2 + (mc^2)^2}} \quad \text{(Relativistic, Momentum)} \] \[ v = at \quad \text{(Classical, Mass and Acceleration)} \]

Explanation: Select a method, input values in your chosen units, and the calculator converts to base units (J, kg, kg·m/s, m/s², s), applies the appropriate formula, and outputs velocity in m/s, km/s, mph, % of \(c\), and Hz.

Unit Conversions:

1 eV = \(1.60218 \times 10^{-19}\) J, 1 MeV = \(1.60218 \times 10^{-13}\) J, 1 GeV = \(1.60218 \times 10^{-10}\) J
1 eV/c² = \(1.78266 \times 10^{-36}\) kg, 1 MeV/c² = \(1.78266 \times 10^{-30}\) kg, 1 GeV/c² = \(1.78266 \times 10^{-27}\) kg
1 eV/c = \(5.34429 \times 10^{-22}\) kg·m/s, 1 MeV/c = \(5.34429 \times 10^{-16}\) kg·m/s, 1 GeV/c = \(5.34429 \times 10^{-13}\) kg·m/s
1 km/s = 1000 m/s, 1 mph = 0.44704 m/s, % of \(c\) = (velocity / \(3 \times 10^8\)) * 100
1 m/s = \(\frac{1}{2\pi}\) Hz (for frequency context)

3. Importance of Particles Velocity

Details: Particle velocity is crucial for understanding motion in physics. Examples include:

Particle accelerators, where electrons or protons reach near-light speeds.
Cosmic rays, studying high-energy particles from space.
Material science, analyzing particle interactions in solids or plasmas.

Applications: Essential for high-energy physics, radiation detection, and quantum mechanics.

4. Using the Calculator

Tips: Select a method, enter positive values with up to 4 decimal places, and choose units. Results are in m/s, km/s, mph, % of \(c\), and Hz. Values < 0.0001 use scientific notation. Avoid zero mass or invalid inputs. Relativistic formulas apply if speeds approach \(c\) (kinetic energy or momentum high relative to rest mass).

Example: For an electron with \(E_k = 1 \, \text{MeV}\), \(m = 0.511 \, \text{MeV}/c^2\):

\(E_k = 1.60218 \times 10^{-13} \, \text{J}\), \(m = 9.10938 \times 10^{-31} \, \text{kg}\)
\(\gamma \approx 1.995\), relativistic: \(v \approx 2.816 \times 10^8 \, \text{m/s}\)
\(v \approx 0.9387 \, \text{of } c\), \(281.6 \, \text{km/s}\), \(629,888.0 \, \text{mph}\), \(4.484 \times 10^7 \, \text{Hz}\)

5. Related Concepts

Relativistic Energy: Total energy \(E = \gamma mc^2\), where \(\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}\).

Relativistic Momentum: \(p = \gamma mv\), linked to velocity via mass and speed.

Particle Acceleration: \(a = \frac{F}{m}\), affecting velocity over time, used in the acceleration method.

6. Frequently Asked Questions (FAQ)

Q: Why use relativistic formulas?
A: For speeds > 0.1% of \(c\), relativistic effects matter; the calculator switches automatically if kinetic energy or momentum indicates high speed.

Q: Can velocity exceed \(c\)?
A: No, relativistic formulas ensure \( v \leq c \).

Q: Why does the result show zero?
A: If mass is zero or inputs are invalid, results default to zero.

Q: Why are some results in scientific notation?
A: Values < 0.0001 are displayed as, e.g., \(1.23 \times 10^{-5}\), for clarity.

Q: What does Hz mean here?
A: Hz is included as \( v / 2\pi \), representing frequency (non-standard but per request), assuming a cyclical context.