QuestionJune 30, 2025

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at 3.80% of the speed of light. Wavelength=square m b. Calculate the velocity of a neutron with a wavelength of 57 pm (1pm=10^-12m) Velocity=square m/s

Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at 3.80% of the speed of light. Wavelength=square m b. Calculate the velocity of a neutron with a wavelength of 57 pm (1pm=10^-12m) Velocity=square m/s
Neutron diffraction is used in determining the structures of molecules. a. Calculate the de Broglie wavelength of a neutron moving at 3.80% of the speed of light. Wavelength=square m b. Calculate the velocity of a neutron with a wavelength of 57 pm (1pm=10^-12m) Velocity=square m/s

Solution
4.2(209 votes)

Answer

a. Wavelength = 3.32 \times 10^{-11} \text{ m} ### b. Velocity = 6.95 \times 10^3 \text{ m/s} Explanation 1. Calculate the de Broglie wavelength for part (a) Use **de Broglie wavelength formula**: \lambda = \frac{h}{mv}, where h = 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s}, m = 1.675 \times 10^{-27} \text{ kg} (mass of neutron), and v = 0.038c with c = 3.00 \times 10^8 \text{ m/s}. Calculate v = 0.038 \times 3.00 \times 10^8 = 1.14 \times 10^7 \text{ m/s}. Then, \lambda = \frac{6.626 \times 10^{-34}}{1.675 \times 10^{-27} \times 1.14 \times 10^7}. 2. Calculate the velocity for part (b) Rearrange **de Broglie wavelength formula** to find v: v = \frac{h}{m\lambda}. Given \lambda = 57 \times 10^{-12} \text{ m}, calculate v = \frac{6.626 \times 10^{-34}}{1.675 \times 10^{-27} \times 57 \times 10^{-12}}.

Explanation

1. Calculate the de Broglie wavelength for part (a)<br /> Use **de Broglie wavelength formula**: $\lambda = \frac{h}{mv}$, where $h = 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s}$, $m = 1.675 \times 10^{-27} \text{ kg}$ (mass of neutron), and $v = 0.038c$ with $c = 3.00 \times 10^8 \text{ m/s}$. Calculate $v = 0.038 \times 3.00 \times 10^8 = 1.14 \times 10^7 \text{ m/s}$. Then, $\lambda = \frac{6.626 \times 10^{-34}}{1.675 \times 10^{-27} \times 1.14 \times 10^7}$.<br /><br />2. Calculate the velocity for part (b)<br /> Rearrange **de Broglie wavelength formula** to find $v$: $v = \frac{h}{m\lambda}$. Given $\lambda = 57 \times 10^{-12} \text{ m}$, calculate $v = \frac{6.626 \times 10^{-34}}{1.675 \times 10^{-27} \times 57 \times 10^{-12}}$.
Click to rate:

Similar Questions