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QuestionFind the de Broglie wavelength of a 145 g ball moving at 36.77 m/s. Round your answer to 3 significant figures.

Studdy Solution

STEP 1

Assumptions1. The mass of the ball is145 g. The velocity of the ball is36.77 m/s3. The ball can be modeled as a single particle4. We will use the de Broglie equation to calculate the wavelength5. The Planck constant (h) is 6.62607015×10−34 m kg/s6.62607015 \times10^{-34} \mathrm{~m}^ \mathrm{~kg} / \mathrm{s}

STEP 2

First, we need to convert the mass of the ball from grams to kilograms, as the Planck constant is in terms of kilograms. We can do this by multiplying the mass in grams by the conversion factor 10− kg/g10^{-} \mathrm{~kg/g}.
Mass=145 g×10− kg/gMass =145 \mathrm{~g} \times10^{-} \mathrm{~kg/g}

STEP 3

Calculate the mass of the ball in kilograms.
Mass=145 g×10−3 kg/g=0.145 kgMass =145 \mathrm{~g} \times10^{-3} \mathrm{~kg/g} =0.145 \mathrm{~kg}

STEP 4

Now, we can use the de Broglie equation to calculate the wavelength. The de Broglie equation is given byλ=hmv\lambda = \frac{h}{mv}where- λ\lambda is the de Broglie wavelength- h is the Planck constant- m is the mass of the particle- v is the velocity of the particle

STEP 5

Plug in the values for the Planck constant, the mass, and the velocity into the de Broglie equation.
λ=.62607015×10−34 m2 kg/s0.145 kg×36.77 m/s\lambda = \frac{.62607015 \times10^{-34} \mathrm{~m}^2 \mathrm{~kg} / \mathrm{s}}{0.145 \mathrm{~kg} \times36.77 \mathrm{~m/s}}

STEP 6

Calculate the de Broglie wavelength.
λ=6.62607015×10−34 m2 kg/s0.145 kg×36.77 m/s=1.24×10−34 m\lambda = \frac{6.62607015 \times10^{-34} \mathrm{~m}^2 \mathrm{~kg} / \mathrm{s}}{0.145 \mathrm{~kg} \times36.77 \mathrm{~m/s}} =1.24 \times10^{-34} \mathrm{~m}The de Broglie wavelength of the ball is 1.24×10−34 m1.24 \times10^{-34} \mathrm{~m} to3 significant figures.

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