The Size of An Atom

Classical Mechanics Level 3

Consider this scaling problem:
A single hydrogen atom at ground state is 1.058 1.058 Å large. This is also represented as 105.8 105.8 picometers or 1.05835442134 × 1 0 − 10 1.05835442134×10^{-10} meters.

It's easy to visualize the number 105.8 or even 106. Much harder to picture 1.05835442134 × 1 0 − 10 1.05835442134×10^{-10} . If you blew up a hydrogen atom to the size of a 12.17 cm 12.17\text{ cm} (or 0.1217 0.1217 m) wide grapefruit (an average grapefruit size), and a real grapefruit grew proportionally, approximately how big would the real grapefruit grow to be?

The same width as the entire Milkyway Galaxy As wide as Earth's moon The same length as an international cargo ship As tall as Everest The same diameter as Jupiter

Christopher Williams by Christopher Williams , 33, USA

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1 solution

For a 1.05835442134 × 1 0 − 10 1.05835442134×10^{-10} m atom to grow to the size of a 12.17 × 1 0 − 2 12.17×10^{-2} m grapefruit, it must grow by a factor of about 1 , 150 , 000 , 000 1,150,000,000 . 12.17 × 1 0 − 2 1.05835442134 × 1 0 − 10 = 1 , 149 , 848 , 828 ≈ 1 , 150 , 000 , 000 \frac{12.17×10^{-2}}{1.05835442134×10^{-10}} = 1,149,848,828 \approx 1,150,000,000

Therefore a real grapefruit of 12.17 × 1 0 − 2 12.17×10^{-2} m would grow by 1 , 150 , 000 , 000 1,150,000,000 . 12.17 × 1 0 − 2 × 1 , 150 , 000 , 000 ≈ 140 , 000 , 000 m 12.17×10^{-2} \times 1,150,000,000 \approx 140,000,000 \text{m}

Jupiter has a diameter of 139 , 822 139,822 km which is ≈ \approx 140 , 000 , 000 140,000,000 m.

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