How many transitions in a hydrogen atom result in the...

Name: Problem 49, Chapter 27: College Physics
Uploaded: 2021-05-07T03:01:29-08:00
Duration: 5 min 12 s
Channel: Sheh Lit Chang
Description: How many transitions in a hydrogen atom result in the absorption of red light: (1) one, (2) two, (3) three, or (4) four? (b) What are the principal quantum numbers of the initial and final states for this process? (c) What are the energy of the required photon and the wavelength of the light associated with it?

How many transitions in a hydrogen atom result in the absorption of red light: (1) one, (2) two, (3) three, or (4) four? (b) What are the principal quantum numbers of the initial and final states for this process? (c) What are the energy of the required photon and the wavelength of the light associated with it?

Key Concepts

Electromagnetic Spectrum and Red Light

The electromagnetic spectrum encompasses all wavelengths of electromagnetic radiation. Red light is a portion of the visible spectrum characterized by longer wavelengths (approximately 620 to 750 nm) and lower photon energies compared to other visible colors. Understanding these properties is important when associating specific atomic transitions with the absorption or emission of red photons.

Photon Energy-Wavelength Relationship

The energy of a photon is directly related to its frequency and inversely related to its wavelength, as described by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This relationship is fundamental in linking the spectral characteristics of light to the energy transitions in atoms.

Hydrogen Atom Energy Levels

In a hydrogen atom, electrons occupy discrete energy levels characterized by specific energy values. These levels are quantized and are typically labeled using the principal quantum number (n), with the energy of each level inversely proportional to the square of n. Transitions between these levels involve the absorption or emission of photons with energies exactly equal to the difference between the levels.

Principal Quantum Number

The principal quantum number, denoted as n, describes the energy level of an electron in an atom. It is a positive integer, and as n increases, the electron’s energy increases and it is found farther from the nucleus. This quantum number is central in determining the spacing between energy levels and the wavelength of the radiative transitions between them.

Photon Absorption and Electron Transitions

Photon absorption in an atom occurs when an electron transitions from a lower energy level to a higher one by absorbing a photon whose energy precisely matches the energy difference between the two states. This concept is essential in understanding spectral lines and the quantization of light absorption, meaning that only those photons with the correct energy will be absorbed.

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