The density of chromium metal is `7.2"g cm"^(-3)`. If the unit cell is cubic with edge length of 289 pm, determine the type of unit cell. Atomic mass of Cr = 52 a.m.u., `N_(0)=6.02xx10^(23)"mol"^(-1)`.

Explanation

`d=7.2"g cm"^(-3),a=289"pm"`
`=2.89xx10^(-8)"cm"`
`N_(A)=6.02xx10^(23)"mol"^(-1)`
`M=52"g mol"^(-1),Z=?`
`d=(ZxxM)/(N_(A)xxa^(3))`
`Z=(d xxN_(A)xxa^(3))/(M)`
`=((7xx2"g cm"^(-3))xx(6xx0.2xx10^(23)"mol"^(-1))xx(2xx89xx10^(-8))^(3)"cm"^(3))/(52"g mol"^(-1))`
`=(7.2xx6.02xx24.14)/(520)=2`
(b.c.c. lattice)