According to the Rydberg Equation, how does the energy of an electron change as it moves further from the nucleus?

The Rydberg Equation is used to describe the energies of the electron transitions in a hydrogen atom. As an electron moves further from the nucleus, it transitions to higher energy levels. In the context of energy levels in an atom, when we refer to energy values, they are often expressed as negative numbers, where the most stable state (closest to the nucleus) has the highest negative value, indicating a bound system.

As the electron moves to higher energy levels (farther from the nucleus), its energy becomes less negative. This change signifies that the electron is gaining energy and becoming less tightly bound to the nucleus. At infinity, where the electron is essentially free, the energy of the electron approaches zero. Thus, the key understanding here is that as an electron moves further away and the energy level increases, the energy becomes less negative.

This concept underscores the relationship between the potential energy of an electron within an atom and its distance from the nucleus, affirming that moving to a higher energy level means a decrease in the magnitude of negative energy, ultimately leading towards a transition to a free state.