Final answer:
The photons from a blue star carry the greatest amount of energy as blue light has the shortest wavelength and the highest frequency, indicating higher energy levels compared to red, yellow, or orange stars. Blue stars are also typically hotter than stars of other colors due to their higher temperatures.
Step-by-step explanation:
Inquiring about the energy of photons from various colored stars, you are touching upon concepts related to the physics of light and stellar classification. The colors of the stars--red, yellow, orange, and blue--are indicative of their surface temperatures, which in turn affect the energy of the photons they emit. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. Given this, blue stars have the shortest wavelengths and highest frequencies, and therefore, the photons emitted from a blue star carry the greatest amount of energy.
When comparing a red dwarf and a yellow dwarf star of equivalent size, the yellow dwarf would typically have a higher temperature. Our own Sun is a yellow dwarf star with its surface temperature contributing to its yellow appearance. Therefore, a red dwarf star would be cooler than a yellow dwarf star because red light has a lower frequency than yellow light.
If using filters that transmit blue, yellow, and red light to measure the brightness of stars, intrinsically bluer stars will appear brighter through the blue filter than through the red filter. Conversely, redder stars will appear brighter through the red filter. Vega, known for its relatively even emission across different wavelengths, would serve as a benchmark for comparison. Stars with colors most similar to Vega would demonstrate relatively equal brightness through these filters.
Finally, the colors of stars observed in the night sky, where blue stars are typically hotter than red ones, further reinforce the concept that a star's temperature dictates its color. Hence, comparing a blue star like Archenar to a red star like Betelgeuse, Archenar would be the hotter star while Betelgeuse would be cooler.