# De Broglie Wavelength of Matter Waves

## Exercises with Solutions

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### Exercise: De Broglie Wavelength of a Bullet

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 $$500 \, \frac{\text m}{\text s}$$.