Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show the ionization limit.

검증된 단계별 안내

Understand the context: The He+ ion is a hydrogen-like ion with a single electron orbiting the nucleus. Its energy levels can be calculated using the formula for hydrogen-like atoms: E_n = -Z² * (13.6 eV) / n², where Z is the atomic number (Z = 2 for helium), n is the principal quantum number, and 13.6 eV is the ionization energy of hydrogen.

Determine the energy levels: For each principal quantum number n (e.g., n = 1, 2, 3, ...), calculate the energy using the formula E_n = -Z² * (13.6 eV) / n². For He+, Z = 2, so the formula becomes E_n = -4 * (13.6 eV) / n². These values represent the energy levels of the electron in the He+ ion.

Draw the energy-level diagram: On the vertical axis, represent energy in electron volts (eV). Start with the lowest energy level (n = 1) at the bottom and progressively add higher energy levels (n = 2, 3, 4, ...) above it. The spacing between levels decreases as n increases, reflecting the inverse square relationship in the formula.

Show the ionization limit: The ionization limit corresponds to the energy level where the electron is completely removed from the atom (n → ∞). In this case, the ionization limit is 0 eV, as the energy levels approach 0 eV as n increases indefinitely. Mark this limit clearly at the top of the diagram.

Label the diagram: Clearly label each energy level with its corresponding principal quantum number (n = 1, 2, 3, ...) and energy value (e.g., E_1, E_2, E_3). Also, label the ionization limit at 0 eV to indicate the point where the electron is no longer bound to the nucleus.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Energy-Level Diagram

An energy-level diagram visually represents the quantized energy states of an atom or ion. Each horizontal line corresponds to a specific energy level, with the lowest level at the bottom. For the He+ ion, these levels indicate the energy required for an electron to occupy various states, including ground and excited states, and help illustrate transitions between them.

Ionization Energy

Ionization energy is the amount of energy required to remove an electron from an atom or ion in its gaseous state. For the He+ ion, this energy corresponds to the transition from the highest occupied energy level to a state where the electron is completely removed, reaching the ionization limit. This concept is crucial for understanding how energy levels relate to the stability and reactivity of ions.

Ionization Limit

The ionization limit is the energy threshold at which an electron can be completely removed from an atom or ion, resulting in the formation of a positively charged ion. In an energy-level diagram, it is represented as a horizontal line above the highest energy level of the ion. For He+, this limit indicates the maximum energy state before ionization occurs, providing insight into the stability of the ion.