What is the approximate shortest internuclear distance between any two carbon atoms in diamond if it has density equal to 2 gm/ml? $[N_{A} = 6 \times 10^{23}]$

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$1.414 \times 10^{- 3} cm$

$0.87 \times 10^{- 23 / 3} cm$

$1.414 \times 10^{- 23 / 3} cm$

$1.73 \times 10^{- 9} cm$

answer is B.

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Detailed Solution

Given, density equal to 2 gm/ml

We know that,

$d = \frac{z \times M}{a^{3} \times N_{A}}$

Here, Z is 8, M is 12 and $N_{A} = 6 \times 10^{23}$ . Put the values,

$2 = \frac{8 \times 12}{a^{3} \times 6 \times 10^{23}} a = 0.87 \times 10^{- 23 / 3} cm$

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