# The De Broglie Wavelength of an Electron

## What is the de Broglie wavelength of an electron traveling at 1.59×10^5 m/s ?

The de Broglie wavelength of an electron traveling at 1.59×10^5 m/s is **0.4547 x 10^-9 m**.

## What is an electron?

An electron is a subatomic particle with elementary electric charge, having a negative value. It is considered as an elementary particle due to its lack of known components or substructure. Electrons are part of the first generation of the lepton particle family.

## The De Broglie Wavelength Calculation

The de Broglie wavelength for a particle with momentum p is given by the formula: λ = h/p. This can also be calculated as λ = h/(mv), where λ is the wavelength, h is the constant, m is the mass of the electron, and v is the speed of the electron.

Given the values: m = 9.11 x 10^-31 kg and v = 1.59 x 10^5 m/s, we can substitute these values into the formula to find the de Broglie wavelength of the electron.

By calculation: λ = (6.626 x 10^-34 J-s) / [(9.11 x 10^-31 kg) * (1.59 x 10^5 m/s)]

Therefore, the de Broglie wavelength of an electron traveling at 1.59×10^5 m/s is **0.4547 x 10^-9 m**.

The de Broglie wavelength concept indicates the length scale at which a particle's wave-like characteristics become significant. It provides insights into the wave-particle duality of matter, showing that particles like electrons exhibit both particle and wave properties.

Understanding the de Broglie wavelength is crucial in quantum mechanics, as it helps in describing the behavior of particles at a quantum level. The calculation of the wavelength involves fundamental constants like Planck's constant and the mass and velocity of the particle.

By determining the de Broglie wavelength of an electron, we can better comprehend its wave nature and the implications for its behavior in various physical phenomena. This knowledge is essential in fields such as physics, chemistry, and quantum computing.