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Grade upto college level Physical Chemistry

The edge length of unit cell of a metal having molecular weight 75 g/mol is 5 Å which crystallizes in cubic lattice. If the density is 2 g/cc then find the radius of metal atom (NA = 6 * 1023). Give the answer in pm.

Profile image of Shane Macguire
12 Years agoGrade upto college level
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2 Answers

Profile image of Deepak Patra
12 Years ago
Hello Student,
Please find the answer to your question
For bcc ; r = √3/2 a;
d = n * M/NAV * a3 or n = d *N AV *a3/M
=> n = 2 *6 *1023 (5 *10-8)3/75 = 2
Therefore Metal crystallizes in BCC structure and for a BCC lattice √3a = 4r
r = √3/4 a = √3 *5/4 = 2.165 Å = 216.5 pm
so the required answer is 217 pm.

Thanks
Deepak patra
askIITians Faculty
Profile image of Kushagra Madhukar
5 Years ago
Dear student,
Please find the answer to your question.
 
For bcc ; r = √3/2 a;
d = n * M/NAV * a3 or n = d *N AV *a3/M
=> n = 2 *6 *1023 (5 *10-8)3/75 = 2
Therefore Metal crystallizes in BCC structure and for a BCC lattice √3a = 4r
r = √3/4 a = √3 *5/4 = 2.165 Å = 216.5 pm
so the required answer is 217 pm.
 
Thanks and regards,
Kushagra