First slide

Crystal lattices and unit cells

Question

Caesium atoms are the largest naturally occurring atoms. The radius of Cs atom is 2.6 $\overset{o}{A}$ . The number of moles of Cs atoms to be laid side by side to give a row of Cs atoms 2.50 cm x × 10^-17 . Find the value of x.

Moderate

Solution

Diameter of Cs $= 2 \times 2.6 = 5.2 Å = 5.2 \times 10^{- 8} cm$
Number of atoms in 2.50 cm 2.50 row = $\frac{2.50}{5.2 \times 10^{- 8}}$
$\begin{aligned} = 0.48 \times 10^{8} \\ = 4.8 \times 10^{7} Cs atoms \end{aligned}$
$∴ Moles of Cs atoms = \frac{4.8 \times 10^{7}}{6 \times 10^{23}} = 0.8 \times 10^{- 16}$
$= 8 \times 10^{- 17}$
$\begin{aligned} ∴ x \times 10^{- 17} = 8 \times 10^{- 17} \\ \Rightarrow x = 8 \end{aligned}$

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