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# Neutron diffraction is used in determining the structures of molecules.a. Calculate the de Broglie wavelength of a neutron moving at 1.00$\%$ of the speed of light.b. Calculate the velocity of a neutron with a wavelength of 75 $\mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{m}\right)$

## a) $\lambda=1.32 \times 10^{-13} \mathrm{m}$b) $v=5300 \mathrm{m} / \mathrm{s}$

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prom 60 Chapter 10 neutrons Defections used in determining the structures of molecules Country to Brookly, wavelength of a neutron moving at 1% of the speed of light. So we're gonna use this equation. Lambda is equal to H and the be so we got as so we're gonna so be, in this case, 1% the speed of light. So we know the speed of light is three times tend to be eight meters per second so 1% as gamy 83 times 10 to the sixth because we have to divide by 100. So Lamda is gonna equal planks constant 6.63 times 10 Judy, they get 34 jewels time seconds allover over the mass of a neutron 1.66 times 10 to the negative 27 kilograms and the three times 10 to be a not a six meters per second. So Landa is going to be equal to That's gonna be 1.3 times 10 to D negative 13 meters. All right. Next, calculate the velocity of a neutron on with a wavelength of 75 Pekka meters. I remember one peak o meter is going to equal Tandy Negative 12 meters. Did we get it? Manipulate this So V is going to equal Lambda Sylvie. It's gonna be ableto h over and Landa which is going to equal 663 times 10 to the negative, 34 jewels Time seconds over 1.66 times 10 to d negative 27 kilograms and then the wavelength that is 75 Pekka meters. So 75 times 10 to the negative 12 meters. That means V is going to be equal to 163 any time sending making 34th body by one point 66 times negative 27 seven times 75 times since the negative 12. Well, that means that your neutron is moving at hi 1003 125 five meters per second.

Manhattan College