Question

What is the de Broglie wavelength?

Answer 1

The de Broglie wavelength is a concept in quantum mechanics that suggests that every moving particle, like an electron or a baseball, can be associated with a wave. This wave is called the "de Broglie wave," and its wavelength is called the de Broglie wavelength.

Louis de Broglie proposed this idea in 1924, suggesting that just like light behaves as both a wave and a particle (called wave-particle duality), matter (particles like electrons) also behaves like a wave under certain conditions.

Formula for de Broglie Wavelength:

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

\[
\lambda = \frac{h}{p}
\]

Where:

1. \(\lambda\) = de Broglie wavelength
   

1. \(h\) = Planck’s constant (\(6.626 \times 10^{-34}\) J·s)
   

1. \(p\) = momentum of the particle (mass × velocity)
   

In simpler terms, this formula means that the wavelength of a particle is inversely proportional to its momentum. The faster or heavier the particle, the shorter its wavelength will be.

Key Points:

1. For small particles like electrons: The de Broglie wavelength is noticeable because their mass is tiny, so their momentum can be small enough for the wave-like nature to be observed.
   

1. For large objects: Like a baseball, the wavelength is extremely small, so it's not noticeable and behaves more like a particle.
   

   

Example:

For an electron moving with a velocity of \(v\), the de Broglie wavelength can be calculated by using the formula \(\lambda = \frac{h}{mv}\), where \(m\) is the mass of the electron.

The concept of the de Broglie wavelength was revolutionary because it helped explain phenomena like electron diffraction, where electrons behave like waves when they pass through a crystal.