Copper crystallizes in a Face-Centered Cubic unit cellarrangement. The atomic ra

Question

Copper crystallizes in a Face-Centered Cubic unit cellarrangement. The atomic radius of a copper atom is 127.8pm.

1) What is the edge length of a unit cell of copper in pm?

2) What is the volume of a unit cell of copper in cm^3?

3) Calculate the density of copper in g/cm^3.

Explanation / Answer

Please Rate Answer Life Saver if this answer is detailed and toyour liking! a. The FCC unit cell consists of 4 atoms. One eighth of a atom at the8 corners of the cubic cell and one half of a atom at the center ofthe six faces. To find the side length a of the cell consider on ofthe faces. It is a square with circle of atomic radius r at itscenter, which is touched by circles of the radius r centered at thecorners. Thus the length of the diagonal is: d = r + 2r + r = 4r from Pythagorean theorem you find: 2a² = d² => a = d / 2 = 8 · r For copper a = 8 · 127.8pm = 361.5pm b The volume of the cubic cell is V_cell = a³ = (361.5pm)³ = (3.615·10^-10m)³ =(3.615·10^-8cm)³ = 4.72·10^-23cm³ c The density is given by the mass of 4 atoms divided by the volumeof the cell: = 4 · m_atom / V_cell = 4 · 63.546 u / 4.72·10^-23cm³ = 4 · 63.546 u / 4.72·10^-23cm³ = 4 · 63.546·1.660538783·10^24 kg /4.72·10^-23cm³ = 8.94g/cm³

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