Multiple Choice
What is the de Broglie wavelength of an electron moving at a velocity of 5.97 × 10^6 m/s? (Assume the mass of an electron is 9.11 × 10^-31 kg and Planck's constant is 6.63 × 10^-34 Js)
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9. Quantum Mechanics
De Broglie Wavelength
Multiple Choice
If an electron has a de Broglie wavelength of 0.250 nm, what is its momentum?
A
2.65 × 10^{-24} kg·m/s
B
6.63 × 10^{-34} kg·m/s
C
1.32 × 10^{-27} kg·m/s
D
9.11 × 10^{-31} kg·m/s
Verified step by step guidance1
Recall the de Broglie wavelength formula that relates a particle's wavelength \(\lambda\) to its momentum \(p\):
\[\lambda = \frac{h}{p}\]
where \(h\) is Planck's constant and \(p\) is the momentum.
Rearrange the formula to solve for momentum \(p\):
\[p = \frac{h}{\lambda}\]
Identify the given values:
- Wavelength \(\lambda = 0.250\) nm (convert this to meters by multiplying by \$10^{-9}$)
- Planck's constant \(h = 6.626 \times 10^{-34}\) J·s
Substitute the values into the momentum formula:
\[p = \frac{6.626 \times 10^{-34}}{0.250 \times 10^{-9}}\]
Calculate the momentum \(p\) using the above expression to find the electron's momentum in kg·m/s.
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