Question

what is the de broglie wavelength (in m) of a 58.1 g tennis ball when served at a velocity of 48.5 m/s?

Explanation:

Step1: Convert mass to SI unit

The mass $m = 58.1\ g=0.0581\ kg$.

Step2: Recall de - Broglie wavelength formula

The de - Broglie wavelength formula is $\lambda=\frac{h}{p}$, where $p = mv$ (momentum) and $h = 6.63\times10^{-34}\ J\cdot s$ (Planck's constant). First, find the momentum $p$.
$p=mv=(0.0581\ kg)\times(48.5\ m/s)=2.81785\ kg\cdot m/s$.

Step3: Calculate the de - Broglie wavelength

$\lambda=\frac{h}{p}=\frac{6.63\times 10^{-34}\ J\cdot s}{2.81785\ kg\cdot m/s}\approx2.35\times 10^{-34}\ m$.

Answer:

$2.35\times 10^{-34}\ m$