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The densities of alkali metals are:
- Lithium (Li): $$0.534 \text{ g cm}^{-3}$$
- Sodium (Na): $$0.971 \text{ g cm}^{-3}$$
- Potassium (K): $$0.862 \text{ g cm}^{-3}$$
- Rubidium (Rb): $$1.532 \text{ g cm}^{-3}$$
- Caesium (Cs): $$1.873 \text{ g cm}^{-3}$$
Arranging in increasing order of density:
$$Li \lt K \lt Na \lt Rb \lt Cs$$
$$0.534 \lt 0.862 \lt 0.971 \lt 1.532 \lt 1.873$$
Note: The general trend in alkali metals is that density increases down the group, but potassium is an anomaly — it is less dense than sodium. This is because the increase in atomic volume of potassium is disproportionately larger compared to its increase in atomic mass.
Therefore, the correct answer is Option A: $$Li \lt K \lt Na \lt Rb \lt Cs$$.
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