Question 40.8: Your de Broglie Wavelength A jogger with mass 65.0 kg is jog......
Your de Broglie Wavelength A jogger with mass 65.0 kg is jogging at 4.00 m/s. What is the jogger’s de Broglie wavelength?
INTERPRET and ANTICIPATE
We model the jogger as a matter wave whose wavelength depends on his momentum. Since a person’s jogging speed is much less than the speed of light, we do not need to use special relativity.
SOLVE
Find the magnitude of the momentum using Equation 10.1.
Substitute this momentum into Equation 40.18 to find the de Broglie wavelength of the jogger.
\begin{aligned}\lambda & =\frac{h}{p} \quad \quad (40.18) \\\lambda & =\frac{6.626 \times 10^{-34} J \cdot s }{260 kg \cdot m / s } \\ \lambda & =2.55 \times 10^{-36} m\end{aligned}CHECK AND THINK
The wavelength of a jogger is about 26 orders of magnitude smaller than the diameter of a single atom \left(\sim 10^{-10} m \right) . This is much too small to be detected, so the wave properties of a jogger can be safely ignored. This is why we are able to model objects as particles on the macroscopic scale.