Potassium has a bcc structure with a nearest | vedclass

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(D) In a $bcc$ structure,the nearest neighbour distance $d$ is related to the edge length $a$ by the formula $d = \frac{a \sqrt{3}}{2}$.Given $d = 4.5

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$908$

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(D) In a $bcc$ structure,the nearest neighbour distance $d$ is related to the edge length $a$ by the formula $d = \frac{a \sqrt{3}}{2}$.Given $d = 4.52 \ \mathring{A}$,so $a = \frac{2 	imes 4.52}{\sqrt{3}} \ \mathring{A} = 5.233 \ \mathring{A} = 5.233 	imes 10^{-10} \ m$.For a $bcc$ unit cell,the number of atoms per unit cell $Z = 2$.The density $ho$ is given by $ho = \frac{Z 	imes M}{N_A 	imes a^3}$.Substituting the values: $M = 39 \ g \ mol^{-1} = 0.039 \ kg \ mol^{-1}$,$N_A = 6.022 	imes 10^{23} \ mol^{-1}$.$ho = \frac{2 	imes 0.039}{(6.022 	imes 10^{23}) 	imes (5.233 	imes 10^{-10})^3} \ kg \ m^{-3}$.$ho \approx 908 \ kg \ m^{-3}$.

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.52 \ \mathring{A}$. Its atomic weight is $39$. Its density (in $kg \ m^{-3}$) will be:

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