Atomic Nucleus Radius

The atomic nucleus is the small, dense region at the center of an atom, consisting of protons and neutrons. The size of the nucleus is much smaller than the overall size of the atom.

The radius of an atom is typically on the order of $10^{-10}$ meters (which is $1$ Angstrom).

The radius of an atomic nucleus is typically on the order of $10^{-15}$ meters (which is $1$ femtometer).

The question asks for the order of the nucleus radius in centimeters (cm). We need to convert meters to centimeters.

We know that $1 \text{ meter} = 100 \text{ centimeters} = 10^2 \text{ cm}$.

So, the radius of an atomic nucleus, which is about $10^{-15} \text{ meters}$, can be converted to centimeters:

$\text{Radius} \approx 10^{-15} \text{ m} \times \left(\frac{10^2 \text{ cm}}{1 \text{ m}}\right)$

$\text{Radius} \approx 10^{-15} \times 10^2 \text{ cm}$

$\text{Radius} \approx 10^{-15+2} \text{ cm}$

$\text{Radius} \approx 10^{-13} \text{ cm}$

Therefore, the order of magnitude of the radius of an atomic nucleus is around $10^{-13}$ cm.

Comparing Options for Atomic Nucleus Radius

Let's compare this calculated order of magnitude with the given options:

• Option 1: $10^{-10}$ cm. This is the order of the entire atom's radius, not the nucleus.
• Option 2: $10^{-13}$ cm. This matches our calculated order of magnitude for the nucleus radius.
• Option 3: $10^{-15}$ cm. This is the order of magnitude in meters, not centimeters.

Based on typical nuclear sizes and the conversion to centimeters, the radius of an atomic nucleus is of the order of $10^{-13}$ cm.