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The frequency of a light wave is a fundamental property that dictates its energy and, consequently, its color in the visible spectrum. According to the equation \( E = h u \), where \(E\) represents energy, \(h\) is Planck's constant, and \(u\) is the frequency, we can see a direct relationship between the frequency and the energy of a photon. This means:

• The higher the frequency, the greater the energy of the photon.
• Conversely, a lower frequency corresponds to a lower energy photon.

This relationship is crucial for understanding why different colors of light carry different amounts of energy. Violet light, residing at the higher frequency end of the visible spectrum, naturally has more energy per photon than red light, which is found at the lower frequency end.

Colors of the visible spectrum are unique because they each have different wavelength and frequency characteristics. The visible spectrum ranges from violet to red, and each color within this range can be distinguished by its specific wavelength and frequency. Red light has a longer wavelength, which correlates with a lower frequency and thus lower energy. On the other hand:

• Violet light has a shorter wavelength.
• This equates to a higher frequency and greater energy per photon.

Because wavelength and frequency are inversely related, these characteristics together determine where a color appears in the spectrum, as well as its energy content. For students trying to understand why certain light behaves differently, noticing these wavelength differences is key in observing their practical effects.

When considering light bulbs of equal power, the number of photons emitted depends on their individual energies, which vary based on the frequency. Power, which is the rate of energy used or transferred, remains constant for both the red and violet bulbs. Given their power is equal:

• Fewer violet photons will be emitted due to their higher energy.
• The red bulb can emit more photons because each one carries less energy.

This means \(n_R > n_V\) because more red photons fill the same energy budget. Therefore, when comparing red and violet light sources of the same power, red light will appear to have a broader distribution of photons making it more numerous than violet light.