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A metal (atomic weight = 75) has cubic c...

A metal (atomic weight = 75) has cubic crystal structure. Its density is `2g*cm^(-3)`. The edge length of the unit cell of the crystal is 5Å. What is the radius of the metal atom?

Text Solution

Verified by Experts

`Z=(rhoxxa^(3)xxN)/M=(2xx(5xx10^(-8))^(3)xx6.022xx10^(23))/75=2`
Therefore, the unit cell of metal crystal is body-centred cubic. Radius of the particle in this unit cell, `r=(asqrt3)/4`
`thereforer=(5xx10^(-8)xxsqrt3)/4=2.165xx10^(-8)`cm = 2.165Å
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