de Broglie Wavelength Calculator

Select Particle:

Enter Velocity (m/s):

Enter Kinetic Energy (eV):

Formulas for Calculating the de Broglie Wavelength

The de Broglie wavelength is the wavelength associated with a particle, inversely proportional to its momentum, reflecting wave-particle duality.

Here are the formulas for calculating the de Broglie wavelength in terms of particle velocity and kinetic energy.

In terms of particle velocity

The de Broglie wavelength \(\lambda\) is given by:

\[\lambda = \frac{h}{mv},\]

where \( h \) is Planck’s constant \((6.62607015 \times 10^{-34} \, \text{J} \cdot \text{s})\), \( m \) is the mass of the particle, and \( v \) is the velocity of the particle.

In terms of kinetic energy (eV)

The de Broglie wavelength \(\lambda\) can also be expressed using the kinetic energy \(E_k\) in electron volts (eV):

\[\lambda = \frac{h}{\sqrt{2mE_k}},\]

where \( E_k \) is the kinetic energy of the particle in joules (J). To convert from electronvolts (eV) to joules, \( E_k (\text{J}) = E_k (\text{eV}) \times 1.602176634 \times 10^{-19} \).

These formulas allow us to calculate the de Broglie wavelength based on either the velocity or the kinetic energy of a particle.