The duration of an excited state electron in a hydrogen atom, or any atom for that matter, can vary significantly depending on the specific excited state and the conditions of the environment. The excited state of an electron in an atom is a temporary state that can decay and transition to a lower energy state, typically the ground state, by emitting a photon.
The lifetime of an excited state electron is governed by the probabilities of various decay processes, such as spontaneous emission, collisional de-excitation, or interaction with external electromagnetic fields. The timescales involved can range from fractions of a second to many years, depending on the specific transition and the environment in which the atom exists.
For example, in the case of hydrogen, the most commonly known excited state is the n=2 to n=1 transition, often referred to as the Balmer series. The electron in the n=2 energy level can spontaneously transition to the n=1 level by emitting a photon with a specific energy corresponding to the wavelength of light in the visible spectrum. The lifetime of the excited electron in this state is relatively short, on the order of nanoseconds to microseconds.
However, it's important to note that these lifetimes are average values and represent the characteristic timescale for the decay process. Individual excited state electrons can undergo transitions and decay at different times due to the probabilistic nature of quantum mechanics. The actual lifetime of a specific excited state electron can be influenced by factors such as the presence of other atoms, temperature, pressure, and external electromagnetic fields.
In summary, the lifetime of an excited state electron in a hydrogen atom, or any atom, depends on the specific excited state and the surrounding environment. It can range from very short timescales, on the order of nanoseconds to microseconds, to longer timescales depending on the specific transition and external factors influencing the decay process.