**The Energy of an Electron**

The energy of an electron in an atom is determined by its energy level or electron shell. The energy level of an electron describes the position of the electron in relation to the nucleus of the atom. The energy of an electron increases as its distance from the nucleus increases.

**Understanding the Energy Levels**

In an atom, electrons exist in specific energy levels or electron shells. These energy levels are represented by the quantum number n, where n can have integer values starting from 1. The energy level with n = 1 is the closest to the nucleus, while higher energy levels have higher values of n and are further away from the nucleus.

**The Ground State and Excited States**

The ground state of an electron is the lowest energy level that an electron can occupy in an atom. In the ground state, electrons occupy the energy level with the lowest possible value of n, which is n = 1. The ground state is the most stable configuration for an electron.

When an electron absorbs energy, it can be excited to a higher energy level. This is known as an excited state. In an excited state, electrons occupy energy levels with higher values of n. For example, if an electron in the ground state with n = 1 absorbs energy, it can be excited to the first excited state with n = 2.

**The Energy of an Electron and its Distance from the Nucleus**

The energy of an electron is inversely proportional to its distance from the nucleus. As the distance between the electron and the nucleus increases, the energy of the electron also increases. This can be understood using the concept of electrostatic attraction between the negatively charged electron and the positively charged nucleus.

When an electron is at an infinite distance from the nucleus, it means that it is completely detached from the atom. In this case, the electron has the maximum possible energy, as it is no longer attracted to the nucleus. Therefore, the energy of an electron is maximum at an infinite distance from the nucleus.

**Conclusion**

In conclusion, the energy of an electron is maximum at an infinite distance from the nucleus. This is because the energy of an electron increases as its distance from the nucleus increases. The ground state is the most stable configuration for an electron, while excited states correspond to higher energy levels.

An electron bound to the nucleus by the mutual attraction between unlike charges, has a negative energy. Its most tightly bound to the nucleus nearer it is to the nucleus. That is an electron has least energy when it is in the n=1 shell. As the electron moves away from the nucleus its energy becomes less and less negative, i.e. its energy increases. When the electron is not under the attractive Coulomb force of the nucleus its potential energy is zero and whatever energy it has now, is kinetic energy, which is always positive. So farther the electron more energy it has.