Potassium has a bcc structure with nearest neighbour distance `4.52overset(@)(A)`. Its atomic mass is 39 g/mole. Its density (in kg/`m^(3)`) will be

Options

A. `454 kg m^(-3)`
B. `804 kg m^(-3)`
C. `852 kg m^(-3)`
D. `908 kg m^(-3)`

Answer

D

Explanation

For bcc, `d=(sqrt(3))/(2)a`
or `a=(2d)/(sqrt(3))=(2xx4.52)/(1.732)=5.219 Å=522` pm
`rho = (z xx M)/(a^(3)xx N_(o)xx10^(-30))`
`= (2xx39)/((522)^(3)xx(6.02xx10^(23))xx10^(-30))`
`= 0.91 g//cm^(3)=910 kg m^(-3)`.
Hence, (D) is the correct answer.