In the context of the hydrogen atom, the statement that the hydrogen atom has its maximum energy when it is located at an infinite distance is not accurate. The energy of the hydrogen atom is actually minimum when the electron is in its lowest energy state, which is called the ground state.
In the hydrogen atom, the electron is bound to the nucleus (a single proton) by the electrostatic attraction between the positive charge of the proton and the negative charge of the electron. According to classical physics, if the electron were to be located at an infinite distance from the nucleus, the attractive force between the proton and electron would be zero, resulting in zero potential energy. However, this is an idealized scenario and does not reflect the behavior of the hydrogen atom according to quantum mechanics.
According to quantum mechanics, the energy levels of the hydrogen atom are quantized, meaning that the electron can only occupy specific energy levels. The ground state of the hydrogen atom corresponds to the lowest energy level, where the electron is closest to the nucleus. As the electron moves to higher energy levels, it becomes farther from the nucleus.
In the hydrogen atom, the energy of the electron is negative, indicating that it is bound to the nucleus. The energy increases (becomes less negative) as the electron moves to higher energy levels, corresponding to an increase in its average distance from the nucleus. Therefore, the maximum energy for the hydrogen atom is reached when the electron is in an excited state at a larger average distance from the nucleus, not at an infinite distance.