Math Snap

STEP 1

Assumptions1. The mass of the ball is $144 \mathrm{~g}$
. The velocity of the ball is $33.87 \mathrm{~m/s}$
3. The ball can be modeled as a single particle4. We use the de Broglie wavelength formula $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant, $m$ is the mass of the particle, and $v$ is the velocity of the particle5. Planck's constant $h =6.62607015 \times10^{-34} \mathrm{~m^ kg / s}$

STEP 2

First, we need to convert the mass of the ball from grams to kilograms, since the units of Planck's constant are in terms of kilograms.
$$m =144 \mathrm{~g} =144 \times10^{-} \mathrm{~kg}$$

STEP 3

Now, we can plug in the values for Planck's constant, the mass, and the velocity into the de Broglie wavelength formula.
$$\lambda = \frac{h}{mv} = \frac{6.62607015 \times10^{-34} \mathrm{~m^2 kg / s}}{144 \times10^{-3} \mathrm{~kg} \times33.87 \mathrm{~m/s}}$$

Calculate the de Broglie wavelength.
$$\lambda = \frac{6.62607015 \times10^{-34} \mathrm{~m^2 kg / s}}{144 \times10^{-3} \mathrm{~kg} \times33.87 \mathrm{~m/s}} =1.37 \times10^{-34} \mathrm{~m}$$The de Broglie wavelength of the ball is $1.37 \times10^{-34} \mathrm{~m}$ to3 significant figures.