Question

the unit cell of Na is bcc and it's density is 0.97g/cm3 what is the radius of sodium atom if the molar mass of Na is 23g/mol ?​

Answer 1

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Density in unit cell can be determined by-

$⇒d = \frac{Z \times M}{ {a}^{3} \times \: N \frac{}{ A } }$

$⇒0.97 = \frac{2 \times 23}{ {a}^{3} \times 6.022 \times {10}^{23} }$

$⇒ {a}^{3} = \frac{2 \times 23}{0.97 \times 6.022 \times {10}^{23} }$

$⇒ {a}^{3} = \frac{46}{5.841 \times {10}^{23} }$

$⇒{a}^{3} = 7.875 \times {10}^{ - 23}$

$⇒ a = (0.7875 \times {10}^{ - 24} {)}^{1/3}$

$:a = 0.26 \times {10}^{ - 8} m$

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