Derive Bragg's equation.

In the following figure of beams, the phases of the beams coincide only when the incident angle equals the reflecting angle. The incident beams are parallel to each other until they reach point Z . When they are at point Z , they strike the surface and travel upwards. At point B the 2nd beam scatters. AB + BC is the distance travelled by the 2nd beam. The extra distance is termed as the integral multiple of the wavelength. nλ = AB + BC We know that AB + BC nλ = 2 AB ------------ (1) Further, D is the hypotenuse of the right ΔABZ . Also AB is the opposite side of θ angle. Hence, AB = d sinθ ------------(2) Substitution of (1) in (2) we get: nλ = 2 d sinθ The equation derived is called Bragg's equation.

Silver crystallizes in FCC lattice. If edge length of the cell is 4.07 × 10 - 8 c m and density is 10.5 g c m - 3 . Calculate the atomic mass of silver.

Given, Edge length of the cell ( a ) = 4.07 × 10 - 8 c m Density d = 10.5 g c m - 3 We also know that: the lattice is FCC type, the number of atoms per unit cell , Z = 4 N A = 6.022 × 10 23 m o le - 1 Using the relation d = Z M a 3 N A Therefore, M = da 3 N A Z = 10 .5 gcm - 3 x 4 .077 × 10 - 8 cm 3 × 6 .022 × 10 23 mole - 1 4 = 107.13 g mole - 1 Therefore, the atomic mass of silver = 107 .13 U