Final answer:
The layers of the solar atmosphere can be ranked from shortest to longest peak emission wavelengths as follows: photosphere, chromosphere, and corona, with the photosphere being the coolest and the corona being the hottest and emitting at the longest wavelengths.
Step-by-step explanation:
To rank the layers of the solar atmosphere in order of increasing wavelengths of their peak emissions, we need to consider the temperature of each layer and the type of emissions it produces. Starting with the layer closest to the Sun's surface, we have the photosphere. The photosphere is where the Sun becomes opaque and where the visible emissions that we see as sunlight originate. Temperature-wise, it's cooler compared to the other two layers.
Next is the chromosphere, identified during a solar eclipse by its reddish glow, primarily due to the strong red spectral line of hydrogen (H-alpha). The chromosphere's spectrum consists of bright emission lines, indicating that this layer is composed of hot gases emitting light at discrete wavelengths. Lastly, the corona is the outermost part of the Sun's atmosphere, observed with X-rays and known for its very high temperatures.
Considering the temperatures and the corresponding emissions at various wavelengths, here is the ranking from shortest to longest peak emission wavelengths: photosphere, chromosphere, and corona.