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Write Brief Answer · Q23

Q.Sodium metal crystallizes in bcc structure with the edge length of the unit cell 4.3×10−84.3 \times 10^{-8}cm. Calculate the radius of sodium atom.

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Step 1. Sodium metal crystallises in a bcc structure, so its atoms touch along the body diagonal, giving the relation 3 a=4r\sqrt{3}\,a = 4r.

Step 2. Rearranging for the radius: r=34ar = \dfrac{\sqrt{3}}{4}a.

Step 3. With a=4.3×10−8a = 4.3\times10^{-8} cm: r=1.73205084×4.3×10−8=0.43301×4.3×10−8=1.862×10−8r = \dfrac{1.7320508}{4}\times4.3\times10^{-8} = 0.43301\times4.3\times10^{-8} = 1.862\times10^{-8} cm. …

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