Multiple Choice
Consider an atom traveling at 1% of the speed of light. The de Broglie wavelength of the atom is found to be 3.32 × 10⁻³ pm. Which element is this?
9. Quantum Mechanics
De Broglie Wavelength
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What is the de Broglie wavelength of a 386 g football thrown at 96.6 km/h?
A
1.2 x 10^-34 m
B
6.7 x 10^-30 m
C
3.5 x 10^-28 m
D
9.8 x 10^-32 m
Verified step by step guidance1
Convert the mass of the football from grams to kilograms by dividing by 1000, since the standard unit of mass in physics is kilograms.
Convert the speed of the football from kilometers per hour to meters per second. Use the conversion factor: 1 km/h = 0.27778 m/s.
Use the de Broglie wavelength formula: λ = h / (m * v), where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 m^2 kg/s), m is the mass in kilograms, and v is the velocity in meters per second.
Substitute the values for Planck's constant, the mass of the football in kilograms, and the velocity in meters per second into the de Broglie wavelength formula.
Simplify the expression to find the de Broglie wavelength of the football. Ensure that the units are consistent and cancel appropriately to yield a result in meters.
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