Arrange the following H atom electron transitions in order...

Arrange the following $\mathrm{H}$ atom electron transitions in order of increasing frequency of the photon absorbed or emitted:
(a) $n=2$ to $n=4$
(b) $n=2$ to $n=1$
(c) $n=2$ to $n=5$
(d) $n=4$ to $n=3$

Key Concepts

Hydrogen Atom Energy Levels

Hydrogen atoms have electrons that exist in discrete energy levels, which are quantized. The energy of each level is determined by the principal quantum number, n, and transitions between these levels cause absorption or emission of photons. This quantization is fundamental to understanding atomic spectra and the behavior of electrons in atoms.

Electron Transitions and Photon Absorption/Emission

When an electron in a hydrogen atom transitions between energy levels, a photon is absorbed (if the electron moves to a higher energy level) or emitted (if it moves to a lower energy level). The energy of the photon corresponds to the difference between the initial and final energy levels, making this process crucial for understanding spectral lines.

Energy Difference and Frequency Relationship

The energy of a photon is directly proportional to its frequency, as described by the equation E = h?, where h is Planck's constant and ? is the frequency. This means that transitions with larger energy differences produce higher frequency photons. Ordering transitions by frequency involves comparing the energy differences between the specific electron levels involved.

Rydberg Formula

The Rydberg formula provides a way to calculate the wavelengths (and thus the frequencies) of the spectral lines of hydrogen. It relates the inverse of the wavelength to the difference between the inverse squares of the principal quantum numbers. This formula is fundamental in predicting the outcome of electron transitions in hydrogen and analyzing its emission or absorption spectra.

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