Comparing a 100W and a 40W light bulb that only emits a specfic frequency

Question

I'm sort of confused by this... let's just say the bulbs only emits green light, and we compare a 40 W and 100 W bulb (identical except one is brighter than the other), since the frequency of light emitted from both bulbs are the same, does it mean that there is more energy packed per photon in the light emitted from the 100 W bulb?

mihirb · Accepted Answer

More mathematically: The energy of a photon of light is $E = hnu$ where $h$ is Planck's constant and $nu$ is its frequency. Both lightbulbs emit the same color light so they have the same frequency $nu$ of photons emanating out of them and thus the photons have the same energy for both bulbs.
However, one bulb has more power than the other which means more energy per unit time (power) is emitted by that bulb. In other words, the bulb with more power emits more photons in a given unit of time.
If $E_1$ is the energy emitted by the first bulb in time $Delta t$ then $E_1 = n_1hnu = P_1 Delta t$ where $n_1$ is the number of photons emanating from the first lightbulb in time $Delta t$ and $P_1$ is the power of the bulb. Similarly, $E_2 = n_2 h nu = P_2 Delta t$.
Therefore, $frac{n_2}{n_1} = frac{P_2}{P_1}$. So the number of photons emitted by the bulb in a time $Delta t$ varies linearly with the power of the bulb.

probably_someone · Answer

Every photon of a particular frequency has the same energy. This means that a 100W source of photons of a specific frequency will emit more photons per second than a 40W source of photons at the same frequency.

Answered by probably_someone on September 6, 2021

John Fletcher · Answer

When you say the bulb emits only green light, I assume you mean the light emitted consists of only a single frequency (or wavelength) of electromagnetic energy, or -equivalently - only photons of a single wavelength (or frequency). This is actually a laser, not a (presumably) incandescent light bulb. Since a photon's energy is directly proportional to its frequency, the 100 watt laser is emitting 150% more photons per unit time than the 40 watt laser.
Historically, this mystery relating to the relationship between the brightness and color of a light-emitting source was a baffling question that Einstein addressed in a paper that provided the theoretical basis for the understanding of the photo-electric effect. In this paper, Einstein demonstrated, that light, which was previously believed to be a purely wave-like form of energy, could also be described as a particle -the photon. This provided on of the first indications that - at the smallest scales - energy and matter had both wave-like and particle-like characteristics. This paper became one of the primary foundations for the revolutionary theories of quantum-mechanics, and also earned Einstein the Nobel Prize in physics.

Comparing a 100W and a 40W light bulb that only emits a specfic frequency

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