A certain metal crystallizes in a lattice described by a body-centered cubic (bcc) unit cell. The lattice constant has been measured by X-ray crystallography to be . Calculate the radius of an atom of . Be sure your answer has significant digits, and be sure it has the correct unit symbol.

Full question:

A certain metal crystallizes in a lattice described by a body-centered cubic (bcc) unit cell. The lattice constant (a, the edge of the unit cell) has been measured by X-ray crystallography to be 360 pm. Calculate the radius of an atom of this metal. Be sure your answer has 3 significant digits, and be sure it has the correct unit symbol.

r= 156 pm

Explanation:

In the body-centered cubic cell, the second layer of spheres fits into the depressions of the  first layer and the third layer into the depressions of the second layer (see the first image in the attachment). The coordination number of each sphere in this structure is 8 (each sphere is in contact  with four spheres in the layer above and four spheres in the layer below). The coordination number is defined as the number of atoms (or ions) surrounding an atom (or ion) in a crystal lattice.

In the second picture in the attachment we can see that the relationship between the atomic radius r and the edge length a in body-centered cubic cell is:

We are given the value of a, which is 360 pm. What we have to do is to clear r and solve the equation:

r= 156 pm

  the   balanced   equation   for   reaction of   ca metal   with   o2 to   produce   cao   is as below

2 ca+ o2→ 2 cao2

  explanation

the reaction is   balanced     since the   number of atoms   in reactant side is   equal to   number of atoms   in   product side.   for   example   they   are 2   atom of   ca in   reactant   side   and   2   atoms of ca   in   the product side.

  the   process   is a   meet the   requirement   of   redox   reaction because :     calcium   is   oxidized   from   oxidation state 0   to 2+   while   oxygen   is reduced from   oxidation   state   0   to 2-

atomic mass = 39

number of neutrons = 20

number of protons= 19

electronic configuration = 1s2 2s2 2p6 3s2 3p6 4s1

the number of electron in first shell = 2

number of electrons in n=3 shell = 8