FHSST Physics/Atomic Nucleus/Composition

What the atom is made of

The Greek word $\alpha \tau o\mu o\nu$ (atom) means indivisible. The discovery of the fact that an atom is actually a complex system and can be broken in pieces was the most important step and pivoting point in the development of modern physics.

It was discovered (by Rutherford in 1911) that an atom consists of a positively charged nucleus and negative electrons moving around it. At first, people tried to visualize an atom as a microscopic analog of our solar system where planets move around the sun. This naive planetary model assumes that in the world of very small objects the Newton laws of classical mechanics are valid. This, however, is not the case.

Figure: 15.1 Probability density $P(r)$ for finding the electron at a distance r from the proton in the ground state of hydrogen atom.

The microscopic world is governed by quantum mechanics which does not have such notion as trajectory. Instead, it describes the dynamics of particles in terms of quantum states that are characterized by probability distributions of various observable quantities.

For example, an electron in the atom is not moving along a certain trajectory but rather along all imaginable trajectories with different probabilities. If we were trying to catch this electron, after many such attempts we would discover that the electron can be found anywhere around the nucleus, even very close to and very far from it. However, the probabilities of finding the electron at different distances from the nucleus would be different. What is amazing: the most probable distance corresponds to the classical trajectory!

You can visualize the electron inside an atom as moving around the nucleus chaotically and extremely fast so that for our mental eyes it forms a cloud. In some places this cloud is more dense while in other places more thin. The density of the cloud corresponds to the probability of finding the electron in a particular place. Space distribution of this density (probability) is what we can calculate using quantum mechanics. Results of such calculation for hydrogen atom are shown in Fig. 15.1 . As was mentioned above, the most probable distance (maximum of the curve) coincides with the Bohr radius.

Quantum mechanical equation for any bound system (like an atom) can have solutions only at a discrete set of energies $E_{1},E_{2},E_{3}\dots <math>$, etc. There are simply no solutions for the energies $E$ in between these values, such as, for instance, $E_{1}<E<E_{2}$. This is why a bound system of microscopic particles cannot have an arbitrary energy and can only be in one of the quantum states. Each of such states has certain energy and certain space configuration, i.e. distribution of the probability. A bound quantum system can make transitions from one quantum state to another either spontaneously or as a result of interaction with other systems. The energy conservation law is one of the most fundamental and is valid in quantum world as well as in classical world. This means that any transition between the states with energies $E_{i}$ and $E_{j}$ is accompanied with either emission or absorption of the energy $\Delta E=|E_{i}-E_{j}|$. This is how an atom emits light.

An electron is a very light particle. Its mass is negligible as compared to the total mass of the atom. For example, in the lightest of all atoms, hydrogen, the electron constitutes only 0.054% of the atomic mass. In the silicon atoms that are the main component of the rocks around us, all 14 electrons make up only 0.027% of the mass. Thus, when holding a heavy rock in your hand, you actually feel the collective weight of all the nuclei that are inside it.