Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. b. Will the light be absorbed or emitted?

Verified step by step guidance

1. insert step 1> Determine the initial and final energy levels of the electron transition. Here, the electron is transitioning from n = 4 (initial) to n = 9 (final).
2. insert step 2> Understand that when an electron moves to a higher energy level (from a lower n to a higher n), it absorbs energy. Conversely, when it moves to a lower energy level, it emits energy.
3. insert step 3> Since the electron is moving from n = 4 to n = 9, it is transitioning to a higher energy level.
4. insert step 4> Conclude that the electron must absorb energy to make this transition.
5. insert step 5> Therefore, light will be absorbed during this transition.

Key Concepts

Energy Levels in Atoms

In an atom, electrons occupy specific energy levels, denoted by quantum numbers (n). The energy associated with these levels increases with n, meaning that higher levels (like n=9) have more energy than lower levels (like n=4). When an electron transitions between these levels, it either absorbs or emits energy in the form of light.

Photon Absorption and Emission

When an electron moves from a lower energy level to a higher one, it absorbs a photon, which provides the necessary energy for the transition. Conversely, when an electron falls from a higher energy level to a lower one, it emits a photon. The direction of energy transfer determines whether light is absorbed or emitted during the transition.

Wavelength and Energy Relationship

The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. A transition from a lower to a higher energy level (n=4 to n=9) indicates that energy is absorbed, resulting in a photon with a specific wavelength corresponding to that energy difference.