Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 3 to n = 2

Verified step by step guidance

1. Identify the initial and final energy levels of the electron in the hydrogen atom. In this case, the electron transitions from n = 3 to n = 2.
2. Recall that energy is emitted when an electron moves from a higher energy level to a lower energy level, and energy is absorbed when it moves from a lower energy level to a higher energy level.
3. Since the electron is moving from n = 3 (higher energy level) to n = 2 (lower energy level), energy will be emitted.
4. Use the Rydberg formula to calculate the energy change: \( \Delta E = -R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_f \) is the final energy level, and \( n_i \) is the initial energy level.
5. Substitute the values \( n_i = 3 \) and \( n_f = 2 \) into the Rydberg formula to find the energy change, confirming that it is negative, indicating emission of energy.

Key Concepts

Energy Levels in Hydrogen

In hydrogen, electrons occupy discrete energy levels, denoted by quantum numbers (n). The energy associated with each level increases with n, meaning that higher levels (larger n) have more energy. When an electron transitions between these levels, it either absorbs or emits energy, depending on whether it moves to a higher or lower energy level.

Photon Emission and Absorption

When an electron transitions from a higher energy level to a lower one, it emits energy in the form of a photon. Conversely, when it moves from a lower to a higher energy level, it absorbs a photon. The energy of the emitted or absorbed photon corresponds to the difference in energy between the two levels involved in the transition.

Calculating Energy Changes

The energy change associated with an electronic transition can be calculated using the formula ΔE = E_final - E_initial, where E is the energy of the respective levels. For hydrogen, the energy of each level can be determined using the Rydberg formula, which allows for the calculation of the energy of the photon emitted or absorbed during the transition.