Which of the following star colors sorts its surface temperature from coolest to hottest

Stars appear to be exclusively white at first glance. But if we look carefully, we can notice a range of colors: blue, white, red, and even gold. In the winter constellation of Orion, a beautiful contrast is seen between the red Betelgeuse at Orion's "armpit" and the blue Bellatrix at the shoulder. What causes stars to exhibit different colors remained a mystery until two centuries ago, when Physicists gained enough understanding of the nature of light and the properties of matter at immensely high temperatures.

Specifically, it was the physics of blackbody radiation that enabled us to understand the variation of stellar colors. Shortly after blackbody radiation was understood, it was noticed that the spectra of stars look extremely similar to blackbody radiation curves of various temperatures, ranging from a few thousand Kelvin to ~50,000 Kelvin. The obvious conclusion is that stars are similar to blackbodies, and that the color variation of stars is a direct consequence of their surface temperatures.

Cool stars (i.e., Spectral Type K and M) radiate most of their energy in the red and infrared region of the electromagnetic spectrum and thus appear red, while hot stars (i.e., Spectral Type O and B) emit mostly at blue and ultra-violet wavelengths, making them appear blue or white.

To estimate the surface temperature of a star, we can use the known relationship between the temperature of a blackbody, and the wavelength of light where its spectrum peaks. That is, as you increase the temperature of a blackbody, the peak of its spectrum moves to shorter (bluer) wavelengths of light. This is illustrated in Figure 1 where the intensity of three hypothetical stars is plotted against wavelength. The "rainbow" indicates the range of wavelengths that are visible to the human eye.

Sorry if this doesn't help but if it does good.

they use tree rings to figure out weather patters.