In an incandescent bulb electricity is forced through a narrow wire that’s really heat resistant. As the electricity runs through that wire the electrons bump into things, making the wire hotter. As the wire gets hotter it starts to fling off photons of various frequencies. Most of them are infrared, which you can’t see, but eventually the wire gets red, orange, then white hot. The majority of the energy in this setup just winds up as heat, never having been used to create any light that you can see.
In an LED electrons are directed over a metaphorical “ledge” from one material to another. As each electron jumps off that ledge it emits one photon, where each of those photons is the same frequency. By sizing that ledge correctly you can make sure that all of those photons are visible. This “one electron, one photon” relationship is perfectly efficient.
The inefficiencies of LEDs are from other sources. Sometimes that photon winds up being absorbed inside the LED before it can make it out, for example, and LEDs need DC electricity while your home is wired with AC, so there needs to be a (less than 100% efficient) converter. There’s also the annoyance that we’d like white light but light isn’t a color that you can make a single photon be. You need a combination of colors. This requires another step, either mixing light from red, green, and blue photons, or using a blue/UV LED that hits a phosphor material, which absorbs those high-frequency photons and emits light across the visible spectrum. This still winds up being orders of magnitude more efficient than incandescent since the system isn’t operating off the principle of “just get really friggin hot and light will happen.”
First why Incandescent bulbs are so inefficient. They operate on the same principle that a glowing piece of wood does in a fire. When things get hot enough, they glow. Same with a bulb filament. In an incandescent light, the Filament can get to around 4500 degrees fahrenheit or 2500 degrees celsius (depending on the color of the light). As you can imagine, most of the electrical energy goes to making heat, not light, so incandescent bulbs are only around 7% efficient. In other words, when you use an incandescent bulb, you are making 93% heat and 7% light.
Instead of relying on thermal radiation, like Incandescent bulbs, LEDs rely on electroluminescence. Electroluminescence is basically when you take a material starved of electrons (the smallest pieces of electrical charge), and feed it electrons, and photons (pieces of light) get released in the process. These days we can make semiconductor materials with regions of excess electrons, and electron “holes”, and make LEDs out of them.
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