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{2 E_{k}}{m}} (Classical, Kinetic Energy)

v = c \sqrt{1 - {(\frac{m c^{2}}{E_{k} + m c^{2}})}^{2}} (Relativistic, Kinetic Energy)

v = \frac{p}{m} (Classical, Momentum)

v = \frac{p c}{\sqrt{(p c)^{2} + (m c^{2})^{2}}} (Relativistic, Momentum)

v = a t (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 = $\frac{1}{2 π}$ 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 $E_{k} = 1 MeV$ , $m = 0.511 MeV / c^{2}$ :

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

5. Related Concepts

Relativistic Energy: Total energy $E = γ m c^{2}$ , where $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$ .

Relativistic Momentum: $p = γ m v$ , 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 $v / 2 π$ , representing frequency (non-standard but per request), assuming a cyclical context.