Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 2 to n = 3 (c) from the n = 9 to the n = 6 state.

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Identify the initial and final energy levels of the electron in the hydrogen atom. Here, the electron transitions from n = 2 to n = 3.

Recall that when an electron moves to a higher energy level (higher n value), it absorbs energy. Conversely, when it moves to a lower energy level, it emits energy.

Since the electron is moving from n = 2 to n = 3, it is transitioning to a higher energy level.

Conclude that energy is absorbed during this transition because the electron is moving to a higher energy state.

Remember that the energy difference between levels can be calculated using the Rydberg formula, but the key concept here is the direction of the transition (lower to higher energy level).

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Energy Levels in Hydrogen

In a hydrogen atom, electrons occupy specific energy levels, denoted by quantum numbers (n). The energy associated with each level increases with n, meaning that higher levels are further from the nucleus and have more energy. Understanding these levels is crucial for determining whether energy is absorbed or emitted during electronic transitions.

Absorption and Emission of Energy

When an electron transitions from a lower energy level (n = 2) to a higher energy level (n = 3), it must absorb energy, typically in the form of a photon. Conversely, when an electron falls from a higher level to a lower one, energy is emitted. This principle is fundamental in understanding how atoms interact with light and other forms of energy.

Photon Energy and the Rydberg Formula

The energy of a photon is related to its frequency and wavelength, described by the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency. The Rydberg formula can be used to calculate the wavelengths of emitted or absorbed light during electronic transitions in hydrogen, providing a quantitative understanding of these processes.