Question

What is the de Broglie wavelength of an electron?

Answer 1

The de Broglie wavelength of an electron (or any particle) is the wavelength associated with the particle due to its wave-like properties. According to de Broglie's hypothesis, every moving particle has a wavelength that is inversely proportional to its momentum.

The formula for calculating the de Broglie wavelength (\(\lambda\)) is:

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

Where:

1. \(\lambda\) is the de Broglie wavelength,
   

1. \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J·s}\)),
   

1. \(p\) is the momentum of the particle.
   

Momentum (\(p\)) is given by:

\[
p = mv
\]

Where:

1. \(m\) is the mass of the electron,
   

1. \(v\) is the velocity of the electron.
   

So, the de Broglie wavelength of an electron can be written as:

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

For an electron:

1. Mass of the electron \(m_e \approx 9.11 \times 10^{-31} \, \text{kg}\),
   

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

To calculate the exact de Broglie wavelength of an electron, you need to know its velocity or momentum. If you have that, you can use this formula to find the wavelength. For example, if an electron is moving at a speed \(v\), substitute that value into the formula to get \(\lambda\).