Which of the following is the average mass density of sodium atom assuming, its size to be about `2.5Å` (use the known values off Avogadro's number and the atomic mass of sodium)

Options

A. `0.64xx10^(3)kg//m^(3)`
B. `8.0xx10^(2)kg//m^(3)`
C. `8.6xx10^(3)kg//m^(3)`
D. `6.4xx10^(5)kg//m^(3)`

Explanation

(A) Average radius of sodium atom,
`r=2.5Å=2.5xx10^(-10)m`
`:.` Volume of sodium atom `=4/3pir^(3)`
`=4/3xx3.14xx(2.5xx10^(-10)^(3)=65.42xx10^(-30)m^(3)`
Massof a mole of sodium `=23g=23xx10^(-3)kg`
One mole contains `6.023xx10^(23)` atoms hence the mass of sodium atom,
`M=(23xx10^(-3))/(6.023xx10^(23))kg=3.82xx10^(-26)kg`
`:.` Average mass density of sodium atom
`rho=M/V=(3.82xx10^(-26))/(65.42xx10^(-30))kgm^(-3)=0.64xx10^(3)kgm^(-3)`