Question

Polonium, the largest member of Group 6A, is a rare radioactive metal that is the only element with a crystal structure based on the Simple Cubic unit cell. The density of Polonium is 9.142 g/cm 3 . Calculate an atomic radius for the Polonium atom based on this data.

Answer 1

The atomic radius is:-
`1.68* 10^(-9)\ cm`

Step-by-step explanation:

The expression for density is:

`\rho=\frac {Z* M}{N_a* {Volume}}`

`N_a=6.023* 10^(23)\ {mol}^(-1)`

M is molar mass of polonium = 209 g/mol

For Simple Cubic unit cell , Z= 1

`\rho` is the density = 9.142 g/cm³

Thus,

`Volume=\frac {Z* M}{N_a* {\rho}}`

`Volume=(1* 209)/(6.023* 10^(23)* 9.142)\ cm^3`

`Volume=(209)/(10^(23)* \:55.062266)\ cm^3`

`Volume=37.95* 10^(-24)\ cm^3`

Also, Volume =
`{(Edge\ length)}^3`

Thus, edge length =
`{Volume}^{(1)/(3)}` =
`\left(37.95* \:\:10^(-24)\right)^{(1)/(3)}\ cm=3.36* 10^(-9)\ cm`

Also, for Simple Cubic unit cell,

`Radius = (Edge\ length)/(2)=(3.36* 10^(-9))/(2)\ cm=1.68* 10^(-9)\ cm`

Hence, the atomic radius is:-
`1.68* 10^(-9)\ cm`