An element having bcc structure has atomic mass 50 u and density `6.81 g cm^(-3)`. Calculate the edge length of the unit cell.

Explanation

The following data is provided :
`z=2, M=50u=50" g mol"^(-1), d="6.81 g cm"^(-3), a=?, N_(A)=6.02xx10^(23)mol^(-1)`
Applying the following relation and substituting the values, we get
`a^(3)=(zxxM)/(dxxN_(A))=(2xx50)/(6.81xx6.02xx10^(23))`
`=(100)/(40.9962)xx10^(-23)`
`"or "a^(3)=2.43xx10^(-23)=24.3xx106(-24)`
`"or "a^(3)=x^(3)xx10^(-24)cm^(3)`
`"or "a=x xx10^(-8)cm`
`"or "a=2.896xx10^(-8)cm`
`"or "a=289.6cm`
`["To find out the cube root of 24.3, use logarithms as given below :"`
Let `x^(3)=24.3`
`"or 3 log x "=log 24.3`
`"or 3 log x = 1.3856"`
`" or log x = 0.4618 or x = Antilog 0.4618"`
`"or x = 2.896."]`