1) X-rays of wavelength 0.125nm hit a crystal. the planes of the crystal are 0.350nm apart. calculate the angles at which diffracted X-rays will be detected. (assume bragg diffraction).
2) In a Compton scattering experiment, the incoming and exiting photons had frequencies 2.2 x 10^18 Hz and 1.4 x 10^18 Hz respectively. what was the kinetic energy of the recoiling electrons in electron volts?
2.ii) How fast would these electrons be travelling? (ignore any relativistic effects)
1) nλ = 2dsin(theta), where n = {1,2,3,...}, d is the distance between layers, λ is the wavelength of the photons and theta is the angle between the surface of the material and the incoming photon.
theta = inverse-sine(nλ/2d)
Sub in the values given and then start at n=1, then n=2, then n=3 etc, until nλ/2d exceeds 1. By doing this here we get: Theta = 10.29, 20.92, 32.40, 45.59, 63.25.
2) I) The kinetic energy of the electrons (or more specifically the GAIN in kinetic energy of the electrons) is the change in energy of the photon. Energy of a photon = h x f where h is planck's constant (in the case use 4.14 x 10^-15 eVs as the value for planck's constant because they ask for the answer in eV) and f is the frequency of the photon.
Change in energy of photon = Final energy - initial energy
Change in energy of photon = 4.14 x 10^-15 x 2.2 x 10^18 - 4.14 x 10^-15 x 1.4 x 10^18
Change in energy of photon = 4.14 x 10^-15 (2.2 x 10^18 - 1.4 x 10^18) = 3.312 x 10^3 eV
Change in energy of the recoiling electrons = 3.312 x 10^3 eV
2) II) Ek (in joules) = 0.5mv^2 = 3.312 x 10^3 x (charge of an electron) = 5.2992 x 10^-16 Joules
Therefore, v = sqrt [ (2 x Ek)/mass of electron] = sqrt [ (2 x 5.2992 x 10^-16)/(9.1 x 10^-31)]
v = 3.41 x 10^7 m/s
Hopefully I didn't make any mistakes. Thanks for the Neap answers
Hope this helps.
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