Find the energy required to excite a hydrogen electron from...

Name: Problem 41, Chapter 27: College Physics
Uploaded: 2021-05-06T14:13:38-08:00
Duration: 3 min 37 s
Channel: Sheh Lit Chang
Description: Find the energy required to excite a hydrogen electron from (a) the ground state to the first excited state and (b) the first excited state to the second excited state. (c) Classify the type of light needed to create each of the transitions.

Find the energy required to excite a hydrogen electron from (a) the ground state to the first excited state and (b) the first excited state to the second excited state. (c) Classify the type of light needed to create each of the transitions.

Key Concepts

Spectral Lines and Light Classification

Each electron transition in an atom produces a photon with a specific wavelength, which determines its position in the electromagnetic spectrum. For instance, transitions in hydrogen from the ground state to the first excited state fall in the ultraviolet region (the Lyman series), while transitions from the first excited state to the second excited state generally fall in the visible region (such as the Balmer series). This classification of light is used to identify and analyze the spectral properties of elements.

Quantized Energy Levels

Atoms, particularly the hydrogen atom, possess discrete energy levels rather than a continuous range. Electrons in the atom can only reside in these specific levels, and the energy associated with each level is given by a quantized value. This concept is fundamental in quantum mechanics and explains why electron transitions occur with specific energy changes.

Bohr Model of the Hydrogen Atom

The Bohr model describes the hydrogen atom as having electrons orbiting the nucleus in specific circular paths or orbits. Each orbit corresponds to a particular energy level, and the energy of an electron in a given orbit is determined by the principal quantum number (n). Transitions between these orbits involve absorption or emission of energy equal to the difference in energy levels.

Photon Absorption and Emission

When an electron transitions between different energy levels, it must absorb or emit a photon whose energy matches the difference between those levels. This principle allows us to calculate the energy required for an electronic transition by taking the difference between the initial and final energy levels. It is also the basis of phenomena like spectral lines in atomic spectra.

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