Many metals pack in cubic unit cells. The density of a metal and length of the u

Question

Many metals pack in cubic unit cells. The density of a metal and length of the unit cell can be used to determine the type for packing. For example, sodium has a density of 0.968 g/cm3 and a unit cell side length a of 4.29 Å. (1 Å = 1. 10-8 cm.)

(a) How many sodium atoms are in exactly 1 cm3?

(b) How many unit cells are in exactly 1 cm3?

(c) How many sodium atoms are there per unit cell?

The atoms/unit cell suggests that sodium packs as a  ( simple body-centered face-centered )unit cell.

(e) What is the atomic radius of sodium?

Explanation / Answer

A)density of sodium =0.968g/cm3

So mass per cm3=0.968 g

Mass of 1 sodium atom=23 g/mol /6.022*10^23 atom/mol=3.819 * 10^-23 g/atom

No of sodium atoms per cm3=0.968 g/3.8193 * 10^-23 g/atom=0.253 *10^ 23 atoms

B) Volume of one unit cell=side^3=(4.29 *10-8 cm)^3=78.95 *10^-24 Cm3

No of unit cells in 1cm3=1/78.95 *10^-24 Cm3=127.0 *10^20 unit cells

C) No of sodium atoms are there per unit cell=No of sodium atoms per cm3/No of unit cells in 1cm3

                                                                  =0.253 *10^ 23 atoms/127.0 *10^20

                                                                  =0.001992 *10^3=1.99=2 (approx)

atomic radius of sodium(bcc)=r= sqrt(3a2)/4= sqrt(3*(4.29*10^-8 cm)^2)/4=1.857 *10^-4 cm

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.