Understanding Photon Emission and Energy: Red vs Blue Bulbs

Question:

Let nr and nb be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time. What is the relationship between nr and nb?

Answer:

The number of photons emitted by a red bulb is greater than that of a blue bulb of equal power because red photons have less energy due to their longer wavelengths, implying that more red photons must be emitted to convey the same amount of energy as the fewer, higher-energy blue photons.

Explanation:

Photon Emission and Energy: The question relates to the topic of photon emission and energy in the context of bulbs with different colors, which in physics corresponds to different wavelengths of light.

Energy of Photons: When comparing the number of photons emitted by a red bulb and a blue bulb of equal power in a given time, we have to consider the energy of individual photons determined by their wavelength. According to Planck's equation, the energy of a photon is inversely proportional to its wavelength: E = h*c/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength of light.

Red vs Blue Light: Since red light has a longer wavelength than blue light, red photons have less energy compared to blue photons. For two light bulbs of equal power to emit the same amount of energy, the red light bulb must emit more photons, each with lower energy, while the blue light bulb will emit fewer photons, each with higher energy.

Conclusion: Therefore, nr (the number of photons emitted by a red bulb) is greater than nb (the number of photons emitted by a blue bulb), leading to the final answer that nr > nb. The correct option here is c) nr > nb.