1.

An element occurs in bcc structure. It has a cell edge length of 250 pm. Calculate the molar mass if its density is 8.0 g cm^(-3). Also calculate radius of an atom of this element.

Answer»

Solution :a = 250 pm `= 250 xx 10^(-10)` cm, d = 8 `cm^(-3)`, Z = 2 (for BCC), M = ?
`d = (Z xx M)/(a^(3) xx N_(A))`
`8 = (2 xx M)/((250 xx 10^(-10))^(3) (6.022 xx 10^(23)))`
`N = ((250 xx 10^(-10))^(3) xx (6.022 xx 10^(23)))/(2) xx 8`
`M = (9.409 xx 8)/(2) = 37.64 g MOL^(-1)`
For bcc unit CELL,
`4r = sqrt(3)a `
radius, `R = (sqrt(3)a)/(4) = (1.732 xx 250)/(4)`
= 108.25 pm


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