A student in a physics laboratory observes a hydrogen...

A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming this is part of the Balmer series, determine $n_{\mathrm{i}},$ the principal quantum number of the initial state. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Key Concepts

Diffraction Grating

A diffraction grating is an optical tool used to spatially separate light into its component wavelengths through interference. In spectroscopic experiments, it is used to disperse light from a source such that the different wavelengths (colors) can be individually measured, enabling precise determination of spectral lines and associated quantum transitions.

Principal Quantum Numbers

Principal quantum numbers define the energy levels in an atom. They denote the shell in which an electron resides and determine the electron’s energy and relative distance from the nucleus. In hydrogen spectroscopy, transitions between these levels involve changes in principal quantum numbers, and correctly identifying these numbers is crucial for matching observed spectral lines with theoretical predictions.

Hydrogen Atomic Emission Spectrum

This concept pertains to how electrons in a hydrogen atom transition between energy levels, emitting photons with specific wavelengths in the process. The pattern of these wavelengths forms a series (such as the Balmer series) that characterizes the hydrogen spectrum, providing insights into the structure of the atom and the quantization of its energy levels.

Balmer Series and Electron Transitions

The Balmer series is a specific set of electron transitions in hydrogen where electrons fall from higher energy levels (n ? 3) to the level with principal quantum number 2. This series is significant because many of its lines are in the visible region, which allows direct observation and measurement in laboratory experiments, as well as serving as a testing ground for quantum theories.

Transcript

Please give Ace some feedback