Question

(c) An X-ray crystallography demo: We have neither the budget nor the safety measures in place for using an actual X-ray source and crystal for this demo, but luckily we have access to scrap materials from a kitchen that is being renovated! In that kitchen, there is a microwave (which still works!), a bunch of aluminum foil, and (fortuitously!) a large supply of polystyrene. This is great! We can set up a "scaled up version of X-ray crystallography by making a fake crystal using a large polystyrene block, in which we embed aluminum foil balls representing the crystal atoms, arranged in an appropriately-sized lattice representing the array of atoms in the crystal. We can then use microwaves as fake X-rays. A microwave receiver and speaker can then be used to demonstrate 2 or 3 orders of diffraction maxima when the microwaves are directed at some angle theta relative to the normal of the fake crystal. How big should the polystyrene block be, and what should be the spacing of the aluminum foil balls? (We can assume that the microwave is monochromatic, i.e. it emits a single wavelength, withA 12.2 cm.)

Answer 1

If is diffracts, that means it can obey bragg's condition which is given as,

$n\lambda =2dsin\theta$

For, n=1,2,3 is possible for which

$n=1\Rightarrow \lambda =2dsin\theta$

$n=2\Rightarrow 2 \lambda =2dsin\theta\Rightarrow \lambda =dsin\theta$

$n=3\Rightarrow 3 \lambda =2dsin\theta$

For, aluminium its structure is fcc (facecentredcubic -crystal) for which, N =1,3,5,7,9 etc...

Here, for cubic system

$d= \sqrt{N}a$

This much shoud be interplaner spacing for fake crystal