Multiple Choice
At what speed must an electron travel for its de Broglie wavelength to be 1.0 nm?
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9. Quantum Mechanics
De Broglie Wavelength
Multiple Choice
Consider an atom traveling at 3.00 x 1015 m/s. The de Broglie wavelength is found to be 7.1316 x 10-39. Determine the mass (in g) of the atom.
A
3.10 × 10–6 g
B
6.20 × 10–8 g
C
3.10 × 10–8 g
D
4.45 × 10–7 g
Verified step by step guidance1
Start by recalling the de Broglie wavelength formula: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant (6.626 x 10^-34 Js), \( m \) is the mass of the particle, and \( v \) is the velocity of the particle.
Rearrange the formula to solve for mass \( m \): \( m = \frac{h}{\lambda v} \).
Substitute the given values into the equation: \( h = 6.626 \times 10^{-34} \) Js, \( \lambda = 7.1316 \times 10^{-39} \) m, and \( v = 3.00 \times 10^{15} \) m/s.
Calculate the mass \( m \) using the rearranged formula: \( m = \frac{6.626 \times 10^{-34}}{7.1316 \times 10^{-39} \times 3.00 \times 10^{15}} \).
Convert the mass from kilograms to grams by multiplying the result by 1000, since 1 kg = 1000 g.
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