Determine the energy, frequency, and wavelength of a photon whose absorption changes a He^ ^+ io

step 1 Our question has asked us to find the energy, frequency, and wavelength of a photon whose absorp

Determine the energy, frequency, and wavelength of a photon...

Key Concepts

Energy Difference Calculation for Atomic Transitions

To determine the energy of the absorbed photon in an atomic transition, one must calculate the difference between the energy levels involved. For hydrogen-like ions, these levels are determined by quantum mechanics and the Bohr model, with the transition energy computed from the difference between the initial and final state energy values.

Relationship Between Frequency and Wavelength

The relationship between frequency and wavelength of a photon is given by the equation c = f?, where c is the speed of light, f is the frequency, and ? is the wavelength. This connection allows the determination of the photon’s wavelength once its frequency (or energy) is known, making it crucial for linking the properties of electromagnetic radiation.

Photon Energy and Planck’s Relation

The energy of a photon is directly related to its frequency by Planck’s relation, expressed as E = hf, where E is the photon’s energy, h is Planck’s constant, and f is the frequency. This fundamental relation connects the quantized nature of electromagnetic radiation with the energy changes observed in atomic transitions.

Quantum Energy Transitions

Quantum energy transitions refer to the process in which an electron absorbs or emits energy as it moves between discrete energy levels in an atom. When an electron absorbs a photon, it moves from a lower energy state to a higher energy state; the energy of the photon must precisely match the difference between these levels.

Hydrogen?Like Ion Energy Levels

Hydrogen-like ions, such as He?, possess energy levels similar to the hydrogen atom due to having a single electron, but their energy levels are shifted because of the increased nuclear charge. The energies are quantized and can be described by a modified version of the Bohr model, where the energy scales with the square of the nuclear charge (Z²), leading to discrete energy states that can be calculated using the appropriate formula.

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