A narrow stream of electrons with kinetic enrgy `T= 10keV` passes through a polycrystalline aluminium foil, forming a system of diffraction fringes on a screen. Calculate tha interplanar distacne corresponding to the reflection of third order from a certain system of crystal planes if it is responsible for a diffraction ring of diameter `D= 3.20cm`. The distacnce between the foil and the screen is `l=10.0cm`.

A narrow stream of electrons with kinetic enrgy `T= 10keV` passes thro

1.	A narrow stream of electrons with kinetic enrgy `T= 10keV` passes through a polycrystalline aluminium foil, forming a system of diffraction fringes on a screen. Calculate tha interplanar distacne corresponding to the reflection of third order from a certain system of crystal planes if it is responsible for a diffraction ring of diameter `D= 3.20cm`. The distacnce between the foil and the screen is `l=10.0cm`.
Answer» See the analogous problem with `X`- rays (5.156) The glancing angle is obtained from `tan 2 theta=(D)/(2l)` where `D =` diameter of the ring, `l=` distance from the foil to the screen. Then for the third order Bragg reflection `2 d sin theta=k lambda=k(2pi ħ)/(sqrt(2mT)),(k=3)` Thus `d=(pi ħk)/(sqrt(2mTsin theta))=0.232nm`

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