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A bcc lattic is made up of hollow spheres of X. spheres of soldid 'Y,' are present in hollow spheres of X. The radius of 'Y'is half of the radius of 'X' . Calculate the ratio of the total volume of spherees of 'X' unoccupied by Y in a unitcell and volume of the unit cell ?

Answer» <html><body><p></p>Solution :Let the radius of hollow <a href="https://interviewquestions.tuteehub.com/tag/sphere-1222094" style="font-weight:bold;" target="_blank" title="Click to know more about SPHERE">SPHERE</a> X be r. <br/>As spheres, X have bccstructure, edge lenth `(a)= (<a href="https://interviewquestions.tuteehub.com/tag/4r-319038" style="font-weight:bold;" target="_blank" title="Click to know more about 4R">4R</a>)/(sqrt3)` <br/>Volume of the unit <a href="https://interviewquestions.tuteehub.com/tag/cell-25680" style="font-weight:bold;" target="_blank" title="Click to know more about CELL">CELL</a> = ` a^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) = ( (4r)/(sqrt3))^(3)` <br/>Radius of shphere Y =` r/2 ` (Given )<br/>Volume of Sphere X =` 4/3 <a href="https://interviewquestions.tuteehub.com/tag/pir-591537" style="font-weight:bold;" target="_blank" title="Click to know more about PIR">PIR</a>^(3)`<br/> volume of sphere Y ` 4/3 pi (r/2)^(3)`<br/> Volume of X unoccupied by Y in unit cell = `2 xx [ 4/3 pi r^(3)- 4/3 pi ( r/2)^(3) ]` <br/>( bcc lattice has 2 spheres per unit cell )<br/>` 2xx 4/3 pi r^(3) (1-1/8) = 2xx 4/3 pir^(3) xx 7/8` <br/>`(" Volume of X unoccpied by Y in unit cell")/( " volume of unit cell")= (2xx 4/3 pir^(3) xx7/8)/(((4r)/sqrt3)^(3))= ( (7 pisqrt3))/64`</body></html>


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