QuestionMay 24, 2025

4. What is the de Broglie wavelength of a 1375 kg car traveling at 43km/h

4. What is the de Broglie wavelength of a 1375 kg car traveling at 43km/h
4. What is the de Broglie wavelength of a 1375 kg car traveling at 43km/h

Solution
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Answer

3.98 \times 10^{-38} \text{ m} Explanation 1. Convert speed to meters per second 43 \text{ km/h} = 43 \times \frac{1000}{3600} \text{ m/s} = 11.944 \text{ m/s} 2. Apply de Broglie wavelength formula **\lambda = \frac{h}{mv}**, where h = 6.626 \times 10^{-34} \text{ Js}, m = 1375 \text{ kg}, and v = 11.944 \text{ m/s} \lambda = \frac{6.626 \times 10^{-34}}{1375 \times 11.944} 3. Calculate the wavelength \lambda \approx 3.98 \times 10^{-38} \text{ m}

Explanation

1. Convert speed to meters per second<br /> $43 \text{ km/h} = 43 \times \frac{1000}{3600} \text{ m/s} = 11.944 \text{ m/s}$<br />2. Apply de Broglie wavelength formula<br /> **$\lambda = \frac{h}{mv}$**, where $h = 6.626 \times 10^{-34} \text{ Js}$, $m = 1375 \text{ kg}$, and $v = 11.944 \text{ m/s}$<br /> $\lambda = \frac{6.626 \times 10^{-34}}{1375 \times 11.944}$<br />3. Calculate the wavelength<br /> $\lambda \approx 3.98 \times 10^{-38} \text{ m}$
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