what is the radius of an iron atom? 18) At room temperature, iron crystalizes in

Question

what is the radius of an iron atom?

18) At room temperature, iron crystalizes in a body centered cubic structure. By x-ray diffraction the edge of the cube corresponding to the figure below is found to be 287 pm. What is the radius of an iron atom? Use the Pythagorean theorem to solve for the radius. Use the data provided in the question in addition to the periodic table of the elements and ypour answewr for the radius to to to compute the density of iron. (Consider that Avogandro's number is 6.022x10 23 particles). v3

Explanation / Answer

The edge of corresponding cube is 287pm i.e 287×1012m.

hence l=287×1012 m

Now since it is a BCC structure, we know that,

l 3 is the hypotenuse of right angled triangle,(shaded in the image above) which equals 4r

l 3 = 4r

287×1012 * 3 = 4r

497.1×1012 =4r

r = 124.27×1012 m

The radius of iron atom is 124.27 pm.

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