Electron Speed Calculator

How Do Electrons Accelerate in a Potential?

When an electron moves through a potential difference, the field does work equal to charge times voltage. That work appears as kinetic energy and increases electron speed.

Speed and Wavelength Formulas

Classical (non-relativistic) speed from accelerating potential $V_a$:

$$v = \sqrt{\frac{2 e V_a}{m}}$$

Relativistic speed when corrections matter:

$$v_{\text{rel}} = c\sqrt{1 - \frac{1}{\left(1 + \dfrac{eV_a}{m_0 c^2}\right)^2}}$$

de Broglie wavelength from classical momentum:

$$\lambda = \frac{h}{mv}$$

Example: 100 V gives classical speed near 5930 km/s and wavelength near 0.12 nm. Relativistic effects grow at higher voltages.

Frequently Asked Questions

When is the classical formula accurate?

It works well below about one tenth the speed of light. For higher voltages, use the relativistic formula.

What kinetic energy does 100 V give an electron?

100 electron volts, written 100 eV, because each volt adds one electron volt of energy.

What is de Broglie wavelength?

It is the wavelength associated with a particle's momentum. Faster electrons have shorter wavelengths.

Can magnetic fields accelerate electrons?

Magnetic fields change direction but not speed. Electric fields change kinetic energy and speed.

Why can electrons not reach exactly the speed of light?

Relativistic mass increases with speed, so more energy is needed for each small gain in velocity near c.

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How Do Electrons Accelerate in a Potential?

Speed and Wavelength Formulas

Frequently Asked Questions

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