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QuestionFind the de Broglie wavelength of a 144 g ball moving at 33.87 m/s. Provide the answer to 3 significant figures.

Studdy Solution

STEP 1

Assumptions1. The mass of the ball is 144 g144 \mathrm{~g} . The velocity of the ball is 33.87 m/s33.87 \mathrm{~m/s}
3. The ball can be modeled as a single particle4. We use the de Broglie wavelength formula λ=hmv\lambda = \frac{h}{mv}, where hh is Planck's constant, mm is the mass of the particle, and vv is the velocity of the particle5. Planck's constant h=6.62607015×10−34 mkg/sh =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 g=144×10− kgm =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.
λ=hmv=6.62607015×10−34 m2kg/s144×10−3 kg×33.87 m/s\lambda = \frac{h}{mv} = \frac{6.62607015 \times10^{-34} \mathrm{~m^2 kg / s}}{144 \times10^{-3} \mathrm{~kg} \times33.87 \mathrm{~m/s}}

STEP 4

Calculate the de Broglie wavelength.
λ=6.62607015×10−34 m2kg/s144×10−3 kg×33.87 m/s=1.37×10−34 m\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 1.37×10−34 m1.37 \times10^{-34} \mathrm{~m} to3 significant figures.

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