I have a few chem Problem i cant quite get If anyone can PLE

I have a few chem Problem i cant quite get If anyone can PLEASE Help :)

1. At what angle (in degrees) does first-order diffraction from layers of atoms 225.6 pm apart occur, using x rays with a wavelength of 194 pm?

2. Ar is a solid below -189 ^oC with a face-centered cubic array of atoms and a supposed density of 2.21 g/cm³. Assuming that the atoms are spheres in contact along the face diagonal, what is the radius of a Ar atom (in Angstroms)? An angstrom = 10^-10 m or 10^-8 cm. Hint, first find the length of an edge of the unit cell. (Argon\'s actual density is 1.65 g/cm³.)

3. Hypothetical metal M has a molecular weight 160 g/mol and crystallizes in a body-centered cubic array of atoms in which the length of the unit cell\'s edge is 411.7 pm (10^-12 m). Calculate the density of the metal in g/cm³.

Solution

1) n*lambda= d*sin theta

n=1

sin theta= lambda/d= 194/225.6

theta= 59.3o

2)density= ZM/Noa^3

a^3=4*40/(6.023*10^23)*2.21

a= 4.93*10^-8 cm

r=a/2*sqrt2 = 1.74*10^-8cm= 1.74 Angstroms

3)d=ZM/Noa^3= 2*160/(6.023*10^23)*(411.7*1)^3