Nuclear Radius

Nuclear Radius

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The nuclear radius is a crucial measurement that helps us understand the structure of matter. It determines the smallest scale at which we can describe reality chemically. Although hard to measure the size and shape of a nucleus due to its small scale, there are ways to do it. By estimating the nuclear radius, we can gain a better understanding of the matter's structure. Want to know more about the nuclear radius and how we can estimate it? Keep reading!

How can we define the nuclear radius?

The nuclear radius is a measure of the size of the nucleus of an atom under the assumption that it is approximately spherical.

Under this assumption, the nuclear radius equals the radius (half the diameter) of the nucleus. We can estimate the nuclear radius with theoretical models and experiments. Below, we analyse examples of both and look at how much they agree on the measured/predicted values.

How can we estimate the nuclear radius?

There are several experimental methods we can use to estimate the nuclear radius. We look at two in this explanation: the closest approach method and the electron diffraction method.

Closest approach method

Ernest Rutherford conducted the Rutherford scattering experiment in the early 1900s to study the structure of atoms and provide an atomic model based on experiments. He fired alpha particles at a gold foil and measured their deviation pattern using a screen. Rutherford expected most of the alpha particles to bounce off the gold foil's atoms, but most of them landed behind it. This led to his conclusions that matter is almost empty, the positive charge is concentrated in the nucleus, electrons orbit the nucleus, and the distance between atoms is huge compared to their radius.

One way to estimate the nuclear radius is by studying the energy of an alpha particle during the scattering process. We can find the distance between the alpha particle and the nucleus by equating the potential and kinetic energy contributions and solving for r. However, this closest approach method is due to several reasons, such as overestimating the actual nuclear radius and not accounting for other interactions between alpha particles and nuclei. It is also difficult to send all alpha particles with the same kinetic energy, and neither alpha particles nor the gold foil's nuclei can be treated as point-like charges

Rutherford scattering

Electron diffraction method

Diffraction is a wave-like phenomenon that occurs when waves encounter an object or aperture of similar size or bigger than the wavelength. The de Broglie wavelength formula relates the wavelength of a particle to its mass and speed.

Using electrons instead of alpha particles in a scattering experiment allows for more accurate estimation of the nuclear radius through electron diffraction. This method is not influenced by other interactions since the strong force does not affect electrons, but difficulties include accelerating the electrons to the needed speed and obtaining a diffraction pattern with enough resolution.

Nuclear density depends not only on the number of particles in the nucleus but also on their disposition or "packaging" inside the nucleus. As the number of protons increases, are increasingly more neutrons, and the typical number of neutrons in a nucleus is around 1.5 times the number of protons for heavy elements.

Measuring the nuclear density

By using experimentation to determine the nuclear radius and knowing the masses of protons and neutrons, we can estimate nuclear density under the assumption of uniform spherical spatial distribution. The volume of a sphere in terms of radius r is given by a specific equation, and the number of particles in the nucleus A and their mean mass m can be used to estimate nuclear density ρ. This formula can be applied to all known atoms to estimate the validity of the uniform spherical distribution and explain the distribution of particles inside the nucleus. The symbol for nuclear density is ρ.

A nuclear density plot for a spherically symmetric nucleus
A nuclear density plot for a spherically symmetric nucleus

Key takeaways about nuclear radius include that it is a measure of the size of the nucleus of an atom based on a spherical description. Scattering experiments can be used to estimate nuclear radius, with the closest approach method being a simple but not very accurate option. Electron diffraction is a more method requires experimental setting and Nuclear density is another important quantity for characterizing nuclei and understanding how particles distribute themselves in the nucleus.

Nuclear Radius

What is the nuclear radius?

The nuclear radius is a measure of the size of the nucleus of an atom based on a spherical description.

How does nuclear charge affect the atomic radius?

This is how nuclear charge affects the atomic radius: as the charge increases, the number of particles in the nucleus is higher and their electric repulsion is bigger, which leads to a bigger nuclear radius.

How do you calculate the nuclear radius?

There are several experimental methods to estimate the nuclear radius. Two of them are the closest approach method (less accurate) and the electron diffraction method (more accurate).

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