A hydrogen atom is in the ground state. It absorbs energy...

A hydrogen atom is in the ground state. It absorbs energy and makes a transition to the $n=3$ excited state. The atom returns to the ground state by emitting two photons. What are their wavelengths?

Key Concepts

Cascade Transitions

Cascade transitions occur when an electron does not return directly to the ground state from an excited state but instead undergoes intermediate transitions, emitting more than one photon in the process. This stepwise decay process explains the multiple emitted wavelengths when an atom transitions from a higher excited state to the ground state.

Spectral Series

Spectral series categorize the emission or absorption lines of the hydrogen atom based on the lower energy level involved in the electron's transition. For instance, the Lyman series involves transitions to the ground state (n=1), while the Balmer series involves transitions to the first excited state (n=2). This categorization is essential for predicting and understanding the wavelengths observed in these transitions.

Rydberg Formula

The Rydberg formula is used to calculate the wavelengths of light emitted or absorbed during electron transitions between quantized energy levels in a hydrogen atom. It relates the inverse wavelength to the difference in the reciprocals of the squares of the principal quantum numbers involved in the transition.

Quantum Energy Levels

This concept refers to the discretization of energy states in atoms, where electrons exist in specific orbits with quantized energies. Transitions between these energy levels occur when an atom absorbs or emits a photon, leading to a change in the electron's energy state.

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