Textbook Question
Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 1.25 Å. The mass of a neutron is 1.675×10−27 kg.
9. Quantum Mechanics
De Broglie Wavelength
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A proton in a linear accelerator has a de Broglie wavelength of 132 pm. What is the speed of the proton?
A
4.98 x 10^6 m/s
B
2.50 x 10^7 m/s
C
1.23 x 10^7 m/s
D
3.00 x 10^6 m/s
Verified step by step guidance1
Start by recalling the de Broglie wavelength formula, which relates the wavelength (λ) of a particle to its momentum (p): λ = h / p, where h is Planck's constant (6.626 x 10^-34 m^2 kg/s).
Recognize that momentum (p) can also be expressed as the product of mass (m) and velocity (v) of the particle: p = m * v.
Substitute the expression for momentum into the de Broglie equation: λ = h / (m * v).
Rearrange the equation to solve for velocity (v): v = h / (m * λ).
Substitute the known values into the equation: Planck's constant (h = 6.626 x 10^-34 m^2 kg/s), the mass of a proton (m = 1.67 x 10^-27 kg), and the given wavelength (λ = 132 pm, which is 132 x 10^-12 m). Calculate the velocity using these values.
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