Acertain metal m crystallizes in a lattice described by a body-centered cubic (bcc) unit cell. the lattice constant a has been measured by x-ray crystallography to be 409. calculate the radius of an atom of m.

The radius of the atom is 177.1

Explanation:

A Body-centered cubic lattice (bcc), like all lattices, has lattice points at the eight corners of the unit cell plus an additional points at the center of the cell.

For a body-centered cubic (bcc) unit cell, the formula below can be used to obtain the radius of the atom

a = 4r/√3

where;

a is lattice constant = 409

r is the radius of metal M = ?

From the equation above, make 'r' the  subject of formula

r = (a√3)/4

r = (409*√3)/4

r = 177.1

Therefore, the radius of the atom is 177.1

1. for the first question, we must find the mass of the anhydrous salt, mgso₄. the molar mass for mgso₄·7h₂o is 246.47 g/mol, while that of mgso₄ is 120.37 g/mol.7.834 g mgso₄·7h₂o * 1 mol mgso₄·7h₂o/246.47 g * 1 mol mgso₄/1 mol mgso₄·7h₂o * 20.37 g mgso₄/mol = 0.647 g mgso₄

2. mass of water = mass of sample - mass of anhydrous salemass of water = 7.834 - 0.647 = 7.19 gpercent water in hydrate = 7.19/7.834 * 100 = 91.74%