Assume that one grain of sand has an average size of 1 millimeter across. Based on the chemical composition of sand, can you guess how many atoms are in just one grain of sand? Twenty million? Twenty billion? Keep going. Twenty trillion? Twenty quadrillion? You're not there yet! Twenty quintillion—or the number 2 followed by nineteen zeros—is an approximation of the number of atoms in one grain of sand. But how much is that?

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znk znk · Answer 1 · 2018-09-23T22:37:40+02:00

If we laid each atom end-to-end, they would reach about 20 times the distance from Earth to the Moon.

Assume that sand has a density of 2 g/cm³ and consists of units of SiO₂.

V = 1 mm³ × (1cm/10 mm)³ = 1 × 10⁻³ cm³

Mass = 1 × 10⁻³ cm³ × (2 g/1 cm³) = 2 × 10⁻³ g

Moles of SiO₂ = 2 × 10⁻³ g × (1 mol SiO₂/60.08 g SiO₂) = 3 × 10⁻⁵ mol SiO₂

Units of SiO₂ = 3 × 10⁻⁵ mol SiO₂ × (6.022 × 10²³ units SiO₂/1 mol SiO₂)

= 2 × 10¹⁹ units SiO₂

Atoms = 2 × 10⁻¹⁹ units SiO₂ × (3 atoms/1 unit SiO₂) = 6 × 10¹⁹ atoms

Assume that each atom has a diameter of 140 pm. If we laid them end to end, they would stretch for

6 × 10¹⁹ atoms × (140 × 10⁻¹² m/1 atom) = 8 × 10⁹ m = 8 × 10⁶ km

That’s 20 times the distance from Earth to he Moon.