Under standard conditions of temperature and pressure, chromium (Cr) has a body centred cubic (BCC) crystal structure with a density of 7190kg/m3. a) Given that the atomic mass of chromium is 51.996g/mol, calculate the atomic radius of a chromium atom. b) From literature, find the published value for the atomic radius for chromium. Compare this value to your calculated value and explain any possible differences. Solution a)2 atoms / cell in bcc structure and in 1 mole there are 6 .022 * 10 ^23 atoms density = 7.19 g/cc volume of 1 cell = mass of 2 atoms / density = 51.996 * 2 /(6.022 * 10 ^23 * 7.19) = 2.4 * 10 ^ -23 edge length = 2.88 * 10 ^ -8 cm // cube root of volume = 2.88 A we know that r = a * sqrt(3) /4 = 2.88 * sqrt(3) /4 =1.25 A b) according to literatur it is 1.28 A it\'s not a big difference it arose due to some calculation errors or the some rounding errors in the given values!! I would be thankful if you provide me more points at least 3000 points I did a lot of work on this!! .

1. Under standard conditions of temperature and pressure, chromium (Cr) has a body centred cubic
(BCC) crystal structure with a density of 7190kg/m3.
a) Given that the atomic mass of chromium is 51.996g/mol, calculate the atomic radius of a
chromium atom.
b) From literature, find the published value for the atomic radius for chromium. Compare this
value to your calculated value and explain any possible differences.
Solution
a)2 atoms / cell in bcc structure
and in 1 mole there are 6 .022 * 10 ^23 atoms
density = 7.19 g/cc
volume of 1 cell = mass of 2 atoms / density
= 51.996 * 2 /(6.022 * 10 ^23 * 7.19)
= 2.4 * 10 ^ -23
edge length = 2.88 * 10 ^ -8 cm // cube root of volume
= 2.88 A
we know that r = a * sqrt(3) /4
= 2.88 * sqrt(3) /4
=1.25 A

2. b) according to literatur it is 1.28 A it's not a big difference it arose due to some calculation
errors or the some rounding errors in the given values!!
I would be thankful if you provide me more points at least 3000 points I did a lot of work on
this!!