A hydrogen atom in the ground state absorbs a 13.06 eV...

A hydrogen atom in the ground state absorbs a $13.06 \mathrm{eV}$ photon. Immediately after the absorption, the atom undergoes a quantum jump with $\Delta n=2 .$ What is the wavelength of the photon emitted in this quantum jump?

Key Concepts

Quantum Jumps

Quantum jumps refer to the instantaneous transitions of electrons from one quantized energy level to another, without any intermediate states. These transitions are governed by the specific energy differences between levels, and they occur when the atom interacts with electromagnetic radiation of a matching energy.

Rydberg Formula

The Rydberg formula is an equation used to predict the wavelengths of spectral lines in hydrogen by relating the inverse of the wavelength to the difference in the reciprocals of the squares of the principal quantum numbers involved in the transition. It is a key tool in analyzing the spectral features resulting from electron transitions in hydrogen atoms.

Energy-Wavelength Relationship

The energy of a photon is directly related to its wavelength via the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This relationship enables the conversion between the energy absorbed or emitted during a quantum transition and the corresponding wavelength of the photon.

Hydrogen Atomic Energy Levels

Hydrogen atoms have quantized energy states typically described by the Bohr model, where the energy of each level is inversely proportional to the square of the principal quantum number (n). This quantization means that electrons can only occupy specific energy levels, and transitions between these levels involve discrete amounts of energy.

Photon Emission and Absorption

When an atom absorbs a photon, an electron gains energy and moves to a higher energy level; conversely, when an electron drops to a lower energy level, the atom emits a photon with energy equal to the difference between the two levels. This process is fundamental in understanding atomic spectra and the energy balance within an atom.

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