An electron in the Bohr atom has an energy level determined by the radius of the orbit around the nucleus. The lowest energy state is given by the Bohr radius, which is roughly \(10^{-10} \mathrm{~m}\). The radius of a hydrogen nucleus is about \(10^{-14} \mathrm{~m}\). If the nucleus were the size of a basketball, the size of the atom would be nearest to (A) the size of a small town. (B) the size of a supermarket. (C) the size of a basketball court. (D) the size of a continent. (E) the size of the earth.

To find the ratio, we just need to divide the Bohr radius by the radius of the hydrogen nucleus: \( \frac{10^{-10}\mathrm{~m}} {10^{-14}\mathrm{~m}} = 10^{4} \) This means that the size ratio between the hydrogen atom and its nucleus is 10,000 to 1.

Now we need to find how much larger the basketball is than the hydrogen nucleus. For simplicity, we will assume that a basketball has a radius of about 0.12 m. Then, the scale factor we will use to scale the size of the atom is: \( \frac{0.12\mathrm{~m}} {10^{-14}\mathrm{~m}} = 1.2 \times 10^{15} \)

Multiply the Bohr radius (size of the hydrogen atom) by the scale factor determined in step 2: \( 10^{-10}\mathrm{~m} \times 1.2 \times 10^{15} = 1.2 \times 10^5 \mathrm{~m} \) This corresponds to 120 km.

We can now compare the calculated size of the hydrogen atom (120 km) to the sizes of the given options: (A) the size of a small town: Small towns typically have sizes ranging from 1 to 50 km across. (B) the size of a supermarket: A supermarket is usually much smaller than 1 km. (C) the size of a basketball court: A basketball court is around 0.03 km (30 meters) long. (D) the size of a continent: Continents have sizes ranging from thousands to tens of thousands of kilometers across. (E) the size of the earth: The Earth has a circumference of about 40,000 km. The calculated size of a hydrogen atom (120 km) is nearest to the size of a small town (A). Therefore, the correct answer is (A) the size of a small town.