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Hello students.
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This question belongs to the solid state.
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There is one density formula in a solid state that is density is equal to z.
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Z is the number of atoms present in a unit cell upon molar mass of the compounds upon n avegadro's number multiplied by edge length cube.
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Where a is the edge length.
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Now there are certain parameters given in the question and we have to find out by using this formula.
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In the first part we have to find out the mass of single atom now there are certain parameters that is given in the question that is edge length a is equal to 3 .52 multiply by 10 raised to power minus 8 centimeter and density d is equal to 8 .90 gram per cc 1 gram per cc is equals to 1 gram per cc is equals to 1 gram per centimeter cube so density is expressed in gram per centicumeter cube also.
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And the number of atoms present in the face centered cubic cell z value is equal to 4.
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Now when we have to substitute the given data in the density formula.
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So density is 8 .90 gram per centimeter cube, which is equals to 4 upon m mass upon edge length cube.
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That is 3 .52 multiply by 10 to par minus 8 centimeter whole cube multiplied by the avagadro's number, where m upon n a represents the mass of the single atom, which is equals to 8 .90 gram per centimeter cube multiply by 43 .61 multiply by 10 risk to power minus 244 .4 .61 multiplied by 10 risk to power minus 24 .4.
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Centimeter cube.
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This value comes when we solve this cube this cube value upon four.
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So when we solve this, when we solve this value, the mass of the single atom that is m upon an a value comes to be 9 .07 multiply by 10 rish to power minus 23 gram.
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So here we get the mass of the single atom.
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Now in the b part we have to find out the atomic weight of the metal that is present in a face centered cubic cell.
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Now the formula used to calculate the atomic weight is equal to atomic weight is equal to mass of single atom, multiply by the avagadro's number and knee.
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Now substitute these values, this mass of a single atom we have calculated in the first.
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Part a part which is 9 .07 multiply by 10 raise to power minus 23 gram multiply evergadros number which is 6 .023 into 10 raise to power 23 per mole.
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When we solve this we get the atomic weight which is equal to 58 .44 gram per mole.
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Now after this we have to calculate the radius of the metal which is present in the face centered cubic.
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Now for face centered cubic cell, the relation between the edge length and the radius is, that is 4r is equal to under root 2a.
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Now we have to substitute the values, the given values in order to find out the radius...