Question

True or false? It is impossible for the \(\mathrm{H}^{+}\) cation to exist in an excited state. Justify your answer.

Short answer

True. It is impossible for the \(\mathrm{H}^{+}\) cation to exist in an excited state because the \(\mathrm{H}^{+}\) cation has no electrons. Since there are no electrons, there is no possibility for an electron to be promoted to a higher energy level to create an excited state.

Step-by-step solution

Analyze the electron configuration of the \(\mathrm{H}^{+}\) cation

The \(\mathrm{H}^{+}\) cation is formed when a neutral hydrogen atom loses its only electron. A neutral hydrogen atom has an electron configuration of 1s¹. Since the cation has lost its only electron, the \(\mathrm{H}^{+}\) cation has no electrons in its electron configuration.

Define an excited state

An excited state occurs when an electron in an atom or ion is in a higher energy level than its ground state. For an atom or ion to have an excited state, it must have at least one electron that can be promoted to a higher energy level.

Discuss the possibility of an excited state for the \(\mathrm{H}^{+}\) cation

Since the \(\mathrm{H}^{+}\) cation has no electrons, there is no possibility for an electron to be promoted to a higher energy level. Therefore, it is impossible for the \(\mathrm{H}^{+}\) cation to exist in an excited state.

Conclusion

The statement is true: It is impossible for the \(\mathrm{H}^{+}\) cation to exist in an excited state. This is because the \(\mathrm{H}^{+}\) cation has no electrons, which means there is no possibility for an electron to be promoted to a higher energy level to create an excited state.

Key concepts

Hydrogen Cation H+

The hydrogen cation, denoted as \(\mathrm{H}^{+}\), is simply a proton. It is the result of a neutral hydrogen atom, which consists of one proton and one electron, losing its sole electron. Without any electrons, the \(\mathrm{H}^{+}\) cation lacks the essential component required for electron configurations and subsequent chemical behaviors often observed in other atoms and ions with electrons.

Electron Configuration

Electron configuration refers to the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For neutral hydrogen, the electron configuration is 1s¹, indicating a single electron in the 1s orbital, its lowest energy level. Electron configurations play a critical role in determining how an atom or ion will react chemically and physically with other substances, as the arrangement and movement of electrons govern chemical bonding and properties.

Ground State vs Excited State

Atoms and ions exist in different energy levels or states. The ground state is the lowest energy state, with electrons in the lowest available energy levels following the Aufbau principle. An excited state is any state of the atom or ion where electrons reside in higher energy levels than they do in the ground state. This occurs when energy, often from heat or light, is absorbed by electrons, allowing them to 'jump' to higher orbital levels. For \(\mathrm{H}^{+}\), the concept of excited state does not apply as there are no electrons to be excited.

Atomic Structure

The atomic structure comprises protons and neutrons in the nucleus, surrounded by electrons in orbitals outside the nucleus. An element's chemical characteristics are profoundly influenced by its electron configuration—the distribution of electrons in the atomic orbitals. Protons determine the element's identity, while neutrons add to the atomic mass. Electrons, due to their arrangements and possible migrations between energy levels, define reactivity and bonding. However, for \(\mathrm{H}^{+}\), this atomic structure is minimalistic since it consists of only a nucleus with a single proton and no electrons.