Question

How large is a typical atomic nucleus, and how does the size of the nucleus of an atom compare with the overall size of the atom?

Short answer

The size of a typical atomic nucleus is much smaller than the overall size of the atom. A nucleus radius is approximately 0.003 picometers (pm) while the atomic radius is around 70 pm for a carbon atom. The nucleus occupies a very small space at the center of the atom, with electrons distributed around it.

Step-by-step solution

Understand the composition of an atom

An atom consists of a central nucleus surrounded by electrons in specific energy levels. The nucleus contains protons and neutrons, which are collectively called nucleons. The size of an atom is determined by the distribution of electrons around the nucleus.

Determine the size of a typical atomic nucleus

The size of an atomic nucleus is typically measured in femtometers (\( fm \)). A femtometer is \(10^{-15} meters\). The size of a nucleus depends on the number of nucleons it contains. The approximate radius of a nucleus (in femtometers) can be obtained using the formula: \[ r \approx 1.2 A^{1/3} \] where r is the radius of the nucleus and A is the atomic mass number (number of nucleons). For example, for a carbon atom, with A = 12, the radius of the nucleus is approximately: \[ r \approx 1.2 (12)^{1/3} \approx 3.0 \, fm \]

Determine the overall size of an atom

The overall size of an atom is mainly determined by the distribution of electrons around the nucleus. Typically, atomic radii (distance between the nucleus and the outermost electron) are measured in picometers (\( pm \)), and vary from around 30 pm to 300 pm depending on the element.

Compare the size of the nucleus with the overall size of the atom

Let's compare the approximate size of a carbon atom's nucleus (3 fm) with its overall size (approximately 70 pm for its atomic radius). To make the comparison, we can convert the nucleus radius into picometers: \[ 3 \, fm = 3 \times 10^{-3} \, pm \] So, the nucleus radius is approximately 0.003 pm, while the atomic radius is about 70 pm. The ratio between the nucleus radius and the atomic radius is: \[ \frac{0.003 \, pm}{70 \, pm} \approx 4.3 \times 10^{-5} \] #Conclusion# From the comparison, we can conclude that the size of a typical atomic nucleus is much smaller than the overall size of the atom; it is around 0.003 pm in radius compared to the atomic radius of about 70 pm for carbon. The nucleus occupies a very small space at the center of the atom, while the electrons are distributed around the nucleus.