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CBSE Class 12-science Answered

The unit cell of Na is bcc and its density is 0.97. What is the radius of a sodium atom if the molar mass of Na is 23?
Asked by arushidabhade | 17 Mar, 2021, 01:24: PM
Expert Answer
Density in unit cell can be determined by-
 
straight d equals fraction numerator straight z cross times straight M over denominator straight a cubed cross times straight N subscript straight A end fraction
0.97 equals fraction numerator 2 cross times 23 over denominator straight a cubed cross times 6.022 cross times 10 to the power of 23 end fraction
straight a cubed equals fraction numerator 2 cross times 23 over denominator 0.97 cross times 6.022 cross times 10 to the power of 23 end fraction
straight a cubed equals fraction numerator 46 over denominator 5.841 cross times 10 to the power of 23 end fraction
straight a cubed equals 7.875 cross times 10 to the power of negative 23 end exponent
straight a equals left parenthesis 0.7875 cross times 10 to the power of negative 24 end exponent right parenthesis to the power of 1 divided by 3 end exponent
space straight a equals 0.26 cross times 10 to the power of negative 8 end exponent space straight m
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