Question

if the nucleus of an atom were the size of a soccer ball (70 cm diameter), what would be the diameter of the atom?\
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Explanation:

Step1: Recall the scale of atom and nucleus

The diameter of a nucleus is about \(10^{-15}\) m and the diameter of an atom is about \(10^{-10}\) m. So the ratio of the diameter of an atom to the diameter of its nucleus is \(\frac{10^{-10}\text{ m}}{10^{-15}\text{ m}} = 10^{5}\).

Step2: Calculate the diameter of the atom

Given the diameter of the nucleus (soccer ball) is \(d_{nucleus}=70\) cm. Let the diameter of the atom be \(d_{atom}\). Using the ratio from Step 1: \(d_{atom}=d_{nucleus}\times10^{5}\). Substitute \(d_{nucleus} = 70\) cm: \(d_{atom}=70\times10^{5}\) cm \( = 7\times10^{6}\) cm.

Answer:

\(7\times10^{6}\)