Predict/Calculate An electron in hydrogen absorbs a photon...

Predict/Calculate An electron in hydrogen absorbs a photon and jumps to a higher orbit. (a) Find the energy the photon must have if the initial state is $n=3$ and the final state is $n=5$ . (b) If the initial state was $n=5$ and the final state $n=7,$ would the energy of the photon be greater than, less than, or the same as that found in part (a)? Explain. (c) Calculate the photon energy for part (b).

Key Concepts

Hydrogen Atom Energy Levels

The hydrogen atom has discrete energy levels determined by the principal quantum number n. These levels are quantized, meaning an electron can only exist in specific orbits around the nucleus, each associated with a fixed energy value. Transitions between these levels involve changes in energy that are integral multiples of fundamental constants.

Quantum Transitions and Photon Absorption

When an electron in an atom transitions between energy levels, it either absorbs or emits a photon with energy equal to the difference between the initial and final states. This photon absorption or emission is a cornerstone of quantum mechanics and determines the spectral characteristics observed in hydrogen.

Bohr Model and Energy Quantization

The Bohr model provides the basis for understanding the quantized nature of electron energy levels in hydrogen. It introduces the concept that electrons occupy only certain allowed orbits, and transitions between these orbits occur by absorbing or emitting photons with energy exactly equal to the difference between these quantized levels.

Calculating Transition Energies Using the Rydberg Formula

The Rydberg formula is used to calculate the energy difference between two energy levels in a hydrogen atom by relating the energies of the initial and final states. This relationship, which includes the Rydberg constant, is fundamental for determining the energy of the photon involved in the transition.

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