Electron Velocity Calculator

An Electron Velocity calculator finds an electron's speed with ease. It can use voltage or kinetic energy. You can pick a classic or fast-speed mode. The tool then does the math for you.

This Electron velocity calculator physics tool is useful for study and quick checks. It can also show the energy, gamma value, and the gap between two speed results. NIST provides the key SI and physics constants used in such work.

Electron Velocity Formula

The main electron velocity formula comes from kinetic energy. For a low-speed case, use:

v = √(2KE/mₑ)

If you know the voltage, first use:

KE = eV

So the electron velocity equation becomes:

v = √(2eV/mₑ)

Here, e is the electron charge. V is the input voltage. mₑ is the electron mass.

For a high-speed case, use the relativistic electron velocity calculator mode. First find:

γ = 1 + KE/(mₑc²)

Then find:

v = c√(1 − 1/γ²)

This form keeps the speed below light speed. Relativistic effects can matter more as electron energy rises.

Don't mix this tool with an electron drift velocity calculator. Drift speed is a net flow speed in a wire. Its electron drift velocity equation is:

vᵈ = I/(nqA)

So, the electron drift velocity formula is not the same as the speed from an applied voltage.

How to use online Electron Velocity calculator

1. Pick the Classic or Relativistic mode.
2. Pick voltage or kinetic energy.
3. Enter the value and unit.
4. Click the calc button.
5. Read the speed and other key results.

The tool also works as an electron energy to velocity calculator. It can take eV, keV, MeV, GeV, or J. It can also take V, mV, kV, MV, or GV. The tool first puts each value in its base unit.

Example Electron Velocity calculation

Say an electron gains 100 V.

First find its energy:

KE = eV

KE = 1.602176634 × 10⁻¹⁹ × 100

KE = 1.602176634 × 10⁻¹⁷ J

Now use the velocity of an electron formula:

v = √(2KE/mₑ)

v ≈ 5.93 × 10⁶ m/s

So, the electron speed is about:

5.93 × 10⁶ m/s

At 100 V, the fast-speed result is very close to this value.

Bohr and Hydrogen Note

The electron velocity formula Bohr model uses a set orbit rule. For hydrogen, the velocity of electron in hydrogen atom formula is:

vₙ = αc/n

For the first Bohr orbit, n = 1. This gives a speed near 2.19 × 10⁶ m/s.

The velocity of electron in Bohr orbit formula is not the same as this calculator's voltage rule. The same is true for the velocity of electron formula Bohr model.

An electron thermal velocity calculator is also different. It uses heat or temp. It does not use the same voltage-based rule.

Final Verdict

The Electron Velocity calculator makes speed math quick and clear. It can use energy or voltage. It gives both classic and fast-speed results. Use the classic electron velocity formula in physics for low-speed cases. Use the fast form when speed nears light speed.

FAQs

How to calculate electron velocity?

Use v = √(2KE/mₑ) for a low-speed case. If voltage is known, use KE = eV first.

What is an Electron velocity calculator used for?

It finds an electron's speed from energy or voltage.

Is drift speed the same as electron speed?

No. Drift speed is the net flow of charge in a wire.

Can this tool find Bohr speed?

No. Bohr speed uses a separate atom model.

Is the classical result always safe?

No. At high energy, use the relativistic result.