A ground-state H atom absorbs a photon of wavelength 94.91 nm, and its electron attains a higher

step 1 This question with three parts requires us first to determine what higher level did the electron

A ground-state H atom absorbs a photon of wavelength 94.91...

A ground-state $\mathrm{H}$ atom absorbs a photon of wavelength $94.91 \mathrm{nm},$ and its electron attains a higher energy level. The atom then emits two photons: one of wavelength $1281 \mathrm{nm}$ to reach an intermediate energy level, and a second to return to the ground state. (a) What higher level did the electron reach? (b) What intermediate level did the electron reach? (c) What was the wavelength of the second photon emitted?

A ground-state $\mathrm{H}$ atom absorbs a photon of wavelength $94.91 \mathrm{nm},$ and its electron attains a higher energy level. The atom then emits two photons: one of wavelength $1281 \mathrm{nm}$ to reach an intermediate energy level, and a second to return to the ground state.
(a) What higher level did the electron reach?
(b) What intermediate level did the electron reach?
(c) What was the wavelength of the second photon emitted?

Key Concepts

The Rydberg Formula

The Rydberg formula is used to determine the wavelengths of spectral lines of hydrogen by relating the inverse wavelength to the differences between the inverse squares of the principal quantum numbers. It is a powerful tool for predicting the energies associated with transitions between different energy levels in a hydrogen atom and thus plays a crucial role in the analysis of atomic spectra.

Wavelength-Energy Relationship

The energy of a photon is inversely proportional to its wavelength, as described by the relation E = hc/?, where h is Planck’s constant and c is the speed of light. This concept allows one to calculate the energy absorbed or emitted during an electronic transition in an atom by measuring the wavelength of the photon involved.

Hydrogen Atom Energy Levels

Hydrogen atoms have discrete energy levels that electrons can occupy. These levels are determined by quantum mechanics and are quantized, meaning that electrons can only exist in specific states with defined energies. Transitions between these levels occur when an electron absorbs or emits a photon, with the energy of the photon corresponding exactly to the difference between the initial and final energy levels.

Photon Absorption and Emission

When an atom absorbs a photon, the energy from the photon is used to excite an electron from a lower to a higher energy level. Conversely, when an electron drops from a higher energy level to a lower one, it emits a photon with energy equal to the difference in energy between the two states. This process is governed by the conservation of energy and is fundamental to understanding atomic spectra.

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