Multiple Choice
Calculate the de Broglie wavelength of a hydrogen atom traveling at 495 m/s. Assume the mass of a hydrogen atom is approximately 1.67 x 10^-27 kg.
9. Quantum Mechanics
De Broglie Wavelength
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What is the de Broglie wavelength of an electron moving at a speed of 1.0 × 10^8 m/s?
A
5.45 × 10^-12 m
B
7.27 × 10^-12 m
C
1.45 × 10^-11 m
D
3.63 × 10^-12 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 of the electron \( (9.109 \times 10^{-31} \text{ kg}) \), and \( v \) is the velocity of the electron.
Substitute the given values into the de Broglie wavelength formula. Use \( v = 1.0 \times 10^8 \text{ m/s} \) for the velocity of the electron.
Calculate the denominator of the formula, which is the product of the mass of the electron and its velocity: \( mv = (9.109 \times 10^{-31} \text{ kg}) \times (1.0 \times 10^8 \text{ m/s}) \).
Divide Planck's constant by the result from the previous step to find the de Broglie wavelength: \( \lambda = \frac{6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s}}{mv} \).
Ensure the units are consistent and simplify the expression to find the wavelength in meters. This will give you the de Broglie wavelength of the electron.
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