A hydrogen atom in its ground state is excited to the n=5...

A hydrogen atom in its ground state is excited to the $n=5$ level. It then makes a transition directly to the $n=2$ level before returning to the ground state. (a) What are the wavelengths of the emitted photons? (b) Would any of the emitted light be in the visible region?

Key Concepts

Electromagnetic Spectrum and Visible Light

The electromagnetic spectrum encompasses all wavelengths of electromagnetic radiation, ranging from gamma rays to radio waves. The visible region is a small portion of this spectrum, typically covering wavelengths from about 400 to 700 nanometers. Understanding where a particular photon’s wavelength falls within the spectrum helps determine whether the light is visible to the human eye.

Rydberg Formula

The Rydberg formula is used to calculate the wavelengths of photons emitted or absorbed during electronic transitions in hydrogen-like atoms. It relates the wavelength of the emitted or absorbed light to the inverse difference of the squares of the principal quantum numbers of the initial and final states. This formula is a key tool in predicting spectral lines for hydrogen.

Quantum Energy Levels

In atoms, electrons exist in discrete energy states rather than a continuum, with each level corresponding to a specific amount of energy. Transitions between these quantized levels result in the absorption or emission of energy, typically in the form of photons, and this is a fundamental concept in understanding atomic structure and spectroscopy.

Electron Transitions and Photon Emission

When an electron transitions from a higher energy level to a lower one, the energy difference is released as a photon. The energy of the photon is directly related to the difference between the two energy levels. This principle is used to explain the emission spectrum of atoms, where each photon’s energy (and thus its wavelength) provides information about the specific transition.

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