Multiple Choice
A typical electron velocity is 7.27 x 10^6 m/s. Calculate the de Broglie wavelength of an electron having this velocity:
9. Quantum Mechanics
De Broglie Wavelength
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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.
A
3.67 × 10^-12 m
B
2.27 × 10^-9 m
C
5.12 × 10^-8 m
D
1.45 × 10^-10 m
Verified step by step guidance1
First, understand the concept of de Broglie wavelength, which is given by the formula: λ = h / (mv), where λ is the wavelength, h is Planck's constant (6.626 × 10^-34 Js), m is the mass of the particle, and v is the velocity of the particle.
Identify the given values: the speed of the electron is 3.21 × 10^5 m/s, and the mass of the electron is 9.11 × 10^-31 kg.
Substitute the known values into the de Broglie wavelength formula: λ = (6.626 × 10^-34 Js) / ((9.11 × 10^-31 kg) * (3.21 × 10^5 m/s)).
Perform the multiplication in the denominator: multiply the mass of the electron by its velocity.
Divide Planck's constant by the result from the previous step to find the de Broglie wavelength of the electron.
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