De Broglie Wavelength of Matter Waves

Just like light, a bullet also possesses a wave character, which can be represented by the De Broglie wavelength.

What is the De Broglie wavelength of a bullet with a mass of \( m = 5 \, \text{g} \) flying at a velocity of \( v = 500 \, \frac{\text m}{\text s} \)?

Solution to the Exercise

The De Broglie wavelength is given by: 1 \[ \lambda = \frac{h}{p} \]

Here, \( h = 6.626 \cdot 10^{-34} \, \text{Js} \) is the Planck constant and the momentum \( p = m \cdot v \). Substituting into 1 yields the following relationship: 2 \[ \lambda = \frac{h}{m \cdot v} \]

Now just insert the values from the exercise into 2: 3 \[ \lambda = \frac{6.626 \cdot 10^{-34} \, \text{Js}}{0.005 \, \text{kg} \cdot 500 \, \frac{\text m}{\text s}} = 2.650 \cdot 10^{-34} \, \text{m} \]

So, this wavelength belongs to a \(5 \, \text{g}\) bullet flying at \(500 \, \frac{\text m}{\text s}\).