QuestionJune 10, 2025

What is the de Broglie wavelength of a 11.5 g hummingbird flying at 100. mph? Round your answer to 3 significant digits. 1mile=1.6093km

What is the de Broglie wavelength of a 11.5 g hummingbird flying at 100. mph? Round your answer to 3 significant digits. 1mile=1.6093km
What is the de Broglie wavelength of a 11.5 g hummingbird flying at 100. mph? Round your answer to 3 significant digits. 1mile=1.6093km

Solution
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Answer

1.29 \times 10^{-34} \, \text{m} Explanation 1. Convert mass to kilograms Mass of the hummingbird is 11.5 g. Convert to kg: 11.5 \, \text{g} = 0.0115 \, \text{kg}. 2. Convert speed to meters per second Speed is 100 mph. Convert to m/s: 100 \, \text{mph} \times 1.6093 \, \text{km/mile} \times 1000 \, \text{m/km} \div 3600 \, \text{s/hr} = 44.704 \, \text{m/s}. 3. Apply de Broglie wavelength formula Use **\lambda = \frac{h}{mv}**, where h = 6.626 \times 10^{-34} \, \text{m}^2 \text{kg/s} (Planck's constant), m = 0.0115 \, \text{kg}, and v = 44.704 \, \text{m/s}. Calculate \lambda: \lambda = \frac{6.626 \times 10^{-34}}{0.0115 \times 44.704} = 1.29 \times 10^{-34} \, \text{m}.

Explanation

1. Convert mass to kilograms<br /> Mass of the hummingbird is 11.5 g. Convert to kg: $11.5 \, \text{g} = 0.0115 \, \text{kg}$.<br /><br />2. Convert speed to meters per second<br /> Speed is 100 mph. Convert to m/s: $100 \, \text{mph} \times 1.6093 \, \text{km/mile} \times 1000 \, \text{m/km} \div 3600 \, \text{s/hr} = 44.704 \, \text{m/s}$.<br /><br />3. Apply de Broglie wavelength formula<br /> Use **$\lambda = \frac{h}{mv}$**, where $h = 6.626 \times 10^{-34} \, \text{m}^2 \text{kg/s}$ (Planck's constant), $m = 0.0115 \, \text{kg}$, and $v = 44.704 \, \text{m/s}$.<br /> Calculate $\lambda$: $\lambda = \frac{6.626 \times 10^{-34}}{0.0115 \times 44.704} = 1.29 \times 10^{-34} \, \text{m}$.
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