An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron after the emission?

Verified step by step guidance

1. Identify the initial excited state of the electron, which is given as n = 2.
2. Understand that when an electron emits a photon, it transitions to a lower energy level.
3. Recall that the lowest energy level for a hydrogen atom is n = 1, which is the ground state.
4. Since the electron is initially at n = 2 and emits a photon, it will transition to the next lower energy level.
5. Conclude that the value of n for the electron after the emission is n = 1.

Key Concepts

Quantum States and Energy Levels

In quantum mechanics, electrons in an atom occupy discrete energy levels, denoted by quantum numbers (n). The principal quantum number n indicates the electron's energy level, with lower values corresponding to closer proximity to the nucleus. For hydrogen, these levels are quantized, meaning an electron can only exist in specific states.

Photon Emission

When an electron transitions from a higher energy level to a lower one, it emits energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels. This process is fundamental in understanding how atoms interact with light and is key to phenomena such as spectral lines.

Excited State and Ground State

An excited state refers to an electron being in a higher energy level (n > 1) compared to its ground state, where n = 1. After emitting a photon, the electron returns to a lower energy level, which could be the ground state or another excited state, depending on the energy released. In this case, the electron will return to n = 1 after the emission.