The density of chromium metal is 7.2 g `"cm"^(-3)`. If the unit cell has edge length of 289 pm, determine the type of unit cell. Also calculate the radius of an atom of chromium. (Atomic mass of chromium = 52 a.m.u.)

Explanation

`d=7.2"g cm"^(-3),a=289"pm"`
`=2.89xx10^(-8)"cm"`
`M=52"g mol"^(-1)`
`N_(A)=6.02xx10^(23)"mol"^(-1)Z=?`
`d=(ZxxM)/(a^(3)xxN_(A))`
`=(7xx2"g cm"^(-3)xx(2.89xx10^(-8))^(3)"cm"^(3)xx6.022xx10^(23)"mol"^(-1))/(52"g mol"^(-1))`
`=(7.2xx(2.89)^(3)xx6.022)/(520)`
`=(7.2xx24.14xx6.022)/(520)=2.0`
`therefore` Type of lattice = b.c.c.
For b.c.c. lattice
`sqrt(3)a=4r`
`r=sqrt(3)/(4)a=(1.732xx289)/(4)"pm"`
r = 125.14 pm