Multiple Choice
Calculate the de Broglie wavelength of an electron traveling with a speed of 3.21 × 10^5 m/s. Assume the mass of an electron is 9.11 × 10^-31 kg.
9. Quantum Mechanics
De Broglie Wavelength
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What is the De Broglie wavelength for a 3 g marble rolling at a speed of 30 cm/s?
A
5.55 x 10^-31 m
B
2.21 x 10^-33 m
C
7.37 x 10^-34 m
D
1.11 x 10^-32 m
Verified step by step guidance1
Identify the formula for the De Broglie wavelength: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s} \), \( m \) is the mass in kilograms, and \( v \) is the velocity in meters per second.
Convert the mass of the marble from grams to kilograms. Since 1 gram = 0.001 kilograms, the mass \( m = 3 \text{ g} \times 0.001 \text{ kg/g} = 0.003 \text{ kg} \).
Convert the speed from centimeters per second to meters per second. Since 1 cm = 0.01 m, the speed \( v = 30 \text{ cm/s} \times 0.01 \text{ m/cm} = 0.3 \text{ m/s} \).
Substitute the values into the De Broglie wavelength formula: \( \lambda = \frac{6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s}}{0.003 \text{ kg} \times 0.3 \text{ m/s}} \).
Simplify the expression to find the De Broglie wavelength \( \lambda \).
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