In the Bohr model of the atom, electrons are depicted as traveling in circular orbits, known as shells, around the nucleus, which contains protons and neutrons. The shells are designated by the variable n, representing both the shell number and the energy level of the electrons. Each shell corresponds to a specific potential energy, which is influenced by the distance of the electron from the nucleus.

Central to the Bohr model is the Rydberg constant, which quantifies the energy levels of electrons. When expressed in joules, the Rydberg constant is valued at \( R = 2.178 \times 10^{-18} \) joules. The nucleus, depicted in orange, contains positively charged protons and neutral neutrons, while negatively charged electrons occupy the surrounding shells. The first shell corresponds to n = 1, the second shell to n = 2, and so forth.

The potential energy of an electron in a specific shell can be calculated using the formula:

\( \Delta E = E_n = -R \cdot \frac{Z^2}{n^2} \)

In this equation, \( \Delta E \) represents the change in energy, \( E_n \) is the potential energy of the electron, \( R \) is the Rydberg constant, \( Z \) is the atomic number of the element, and \( n \) is the shell number. For instance, hydrogen, the first element in the periodic table, has an atomic number of \( Z = 1 \). The formula illustrates that the energy of an electron is inversely proportional to the square of its shell number, indicating that electrons in lower shells (closer to the nucleus) have lower potential energy compared to those in higher shells.

Understanding this model allows for the determination of the potential energy associated with any electron in an atom, emphasizing the relationship between an electron's position and its energy within the atomic structure.

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