Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? a. from n = 4 to n = 2

Verified step by step guidance

1. Identify the initial and final energy levels of the electron in the hydrogen atom. Here, the electron transitions from n = 4 (initial) to n = 2 (final).
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 = 4 to n = 2, it is transitioning from a higher energy level to a lower energy level.
4. Conclude that energy is emitted during this transition because the electron is moving to a lower energy state.
5. Use the Rydberg formula to calculate the energy of the emitted photon if needed: \( \Delta E = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant, \( n_1 = 2 \), and \( n_2 = 4 \).

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 (like n=4) have more energy than lower levels (like n=2). Understanding these energy levels is crucial for predicting whether energy is absorbed or emitted during electronic transitions.

Photon Emission and Absorption

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

Rydberg Formula

The Rydberg formula provides a mathematical relationship to calculate the wavelengths of the spectral lines in hydrogen. It is expressed as 1/λ = R(1/n1² - 1/n2²), where R is the Rydberg constant, and n1 and n2 are the principal quantum numbers of the lower and higher energy levels, respectively. This formula helps quantify the energy changes during electronic transitions.