# how many photons emitted from a light bulb **URL:** \ **Category:** Factual Questions\ **Created:** [September 21, 2005, 4:59pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736 "2005-09-21T16:59:40Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![Sigene](https://avatars.discourse-cdn.com/v4/letter/s/df788c/32.png) [@Sigene](https://boards.straightdope.com/u/Sigene)\ **Post date:** [September 21, 2005, 4:59pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/1 "2005-09-21T16:59:40Z")
Lets say its a standard office type fluorescent bulb about 4 ft long. I don’t know how many watts…how about whatever is standard 40? 60? How many photons would be emitted by such a white light source per second? Is it easy to figure out…If so how would one do this? Estimates are fine, I just want a general ball park number that has some credible thought behind it. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [September 21, 2005, 5:16pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/2 "2005-09-21T17:16:34Z")
For a rough ballpark estimate: if your bulb uses 40 watts, that’s 40 Joules in a second. A photon of visible light has a wavelength of around 500 nanometres; since the energy of a photon is given by E = hc/l, where h is Planck’s constant, c is the speed of light, and l is the wavelength, each photon has… ::: calculates ::: about 4 x 10[sup]-19[/sup] Joules. So to emit 40 Joules worth of light in a second, the bulb would have to emit about 10[sup]20[/sup] photons in a second. This is a very rough calculation, of course. To refine it, you’d have to take the efficiency of the bulb into account (not all 40 watts go into light energy), and look at the spectrum of the bulb to figure out exactly what the average photon energy is. I suspect that these factors might cause the final answer to differ by a factor of 10 or so, but not much more than that. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [September 21, 2005, 5:18pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/3 "2005-09-21T17:18:09Z")
Actually, incandescent bulbs are easier. You can ignore the variations in emissivity of the tungsten filament and trweat it like a pure blackbody radiator. According to the **RCA Electro-Optics Handbook** , the spectral radiance in photons per second is n(lambda) = 2c/((lambda)^4)(exp(h(nu)/kT)-1) photons /sec-m^2-steradian-m (p. 36) That gives you the number of photons per wavelength increment. You gotta integrate over wavelengths to get the total number of photons. It’s easier to get the radiant emmittance integrated over all wavelengths and angles in terms of power rather than photons – it follows the simple Stefan-Boltzman equation M(Watts per sq. meter) = (sigma)T^4 sigma is 5.6697 X 10^-8 Watt/m^2-K^4 ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [September 21, 2005, 5:22pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/4 "2005-09-21T17:22:23Z")
For a rough ballpark estimate: if your bulb uses 40 watts, that’s 40 Joules in a second. A photon of visible light has a wavelength of around 500 nanometres; since the energy of a photon is given by E = hc/l, where h is Planck’s constant, c is the speed of light, and l is the wavelength, each photon has… ::: calculates ::: about 4 x 10[sup]-19[/sup] Joules. So to emit 40 Joules worth of light in a second, the bulb would have to emit about 10[sup]20[/sup] photons in a second. This is a very rough calculation, of course. To refine it, you’d have to take the efficiency of the bulb into account (not all 40 watts go into light energy), and look at the spectrum of the bulb to figure out exactly what the average photon energy is. I suspect that these factors might cause the final answer to differ by a factor of 10 or so, but not much more than that. ---
**Author:** ![Squink](https://avatars.discourse-cdn.com/v4/letter/s/b5e925/32.png) [@Squink](https://boards.straightdope.com/u/Squink)\ **Post date:** [September 21, 2005, 6:02pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/5 "2005-09-21T18:02:28Z")
[This site](http://article.dphnet.com/cat-04/lightcompare.shtml) has a table of the photon emission rates of various lamps expressed in microeinsteins per second. An Einstein represents 1 mole (6.02 X 10[sup]23[/sup]) of photons, so a microeinstein is 6.02 X 10[sup]17[/sup] photons. Being a plant site, the values in the table only count photosynthetically active radiation, so there’ll be some photons missed at the red and blue ends of the spectrum: > [@](#): > > The standard measure that quantifies the energy available for photosynthesis is “Photosynthetic Active Radiation” (aka “Photosynthetic Available Radiation”) or PAR. Contrary to the lumen measure that takes into account the human eye response, PAR is an unweighted measure. It accounts with equal weight for all the output a light source emits in the wavelength range between 400 and 700 nm. PAR also differs from the lumen in the fact that it is not a direct measure of energy. It is expressed in “number of photons per second”, whose relationship with “energy per second” (power) is intermediated by the spectral curve of the light source. One cannot be directly converted into the other without the spectral curve. A 40 watt cool white fluorescent puts out about 42.4 microensteins per second. That’s 2.55 X 10[sup]19[/sup] photons per second. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [September 21, 2005, 6:13pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/6 "2005-09-21T18:13:08Z")
So far everyone has based their answer on the electrical power **input** to the bulb. As soon as I can get around to it I’ll try to figure out how many photons are in the light **output** in lumens. ---
**Author:** ![GargoyleWB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gargoylewb/32/199_2.png) [@GargoyleWB](https://boards.straightdope.com/u/GargoyleWB)\ **Post date:** [September 21, 2005, 6:28pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/7 "2005-09-21T18:28:18Z")
You’re referring to **efficacy** , which is usually an empirically derived number for real world purposes, but can be theoretically approximated in many cases. Here’s a page with some good random lighting links and info. The page states a 100W incandescent has an efficay of 17.1 lumens/watt [Light bulb links galore](http://members.misty.com/don/light.html) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 21, 2005, 6:34pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/8 "2005-09-21T18:34:18Z")
> [@](#): > > I suspect that these factors [inefficiency and spectral distribution] might cause the final answer to differ by a factor of 10 or so, but not much more than that. Interestingly, when you take inefficiency into account, you’ll get more photons, not less. Almost all of the energy which goes into a bulb comes out as light. It’s just that only a small amount of it is _visible_ light. Most of the energy is in infrared light, which has less energy per photon. So you’ll need more photons total to carry the same amount of energy. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [September 21, 2005, 6:35pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/9 "2005-09-21T18:35:53Z")
> [@GargoyleWB](#): > > You’re referring to **efficacy** , which is usually an empirically derived number for real world purposes, but can be theoretically approximated in many cases. Here’s a page with some good random lighting links and info. > > The page states a 100W incandescent has an efficay of 17.1 lumens/watt > > [Light bulb links galore](http://members.misty.com/don/light.html) Most packaging gives the light output in lumens for the bulb. The OP asked how many photons of light were put out by a light bulb, not how many photons would be contained in the power input. So far I’ve managed to dig up that 1 candela is 1/643 W/unit solid angle, and 1 candela is 4Pi lumens. Now as soon as I can figure out just what unit solid angle they are talking about (1 steradian?) the rest is a downhill pull. ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [September 21, 2005, 6:44pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/10 "2005-09-21T18:44:50Z")
But all of the power output of an incandescent is in photons. The OP wasn’t clear about ‘visible light’ or not. It’s still a worthy calculation if you’re doing it The candela takes into account the sensitivity of the eye. From [here](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html). > [@Hyperphysics](#): > > The candela is the luminous intensity, in a given direction. of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. The page on the lumen (see ‘light’, then ‘light intensity’) also explains the ‘solid angle’ thing with a diagram. ---
**Author:** ![Sigene](https://avatars.discourse-cdn.com/v4/letter/s/df788c/32.png) [@Sigene](https://boards.straightdope.com/u/Sigene)\ **Post date:** [September 21, 2005, 7:12pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/11 "2005-09-21T19:12:48Z")
> [@panamajack](#): > > The OP wasn’t clear about ‘visible light’ or not. Would it be asking too much for both photons of visible light and all photons? ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [September 21, 2005, 7:21pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/12 "2005-09-21T19:21:15Z")
Your question is complicated by the fact that photons of different color (wavelength) have different energies. So you can’t simply convert output in Watts to numbers of photons without knowing how many photons _of which color_ are present. In the case of blackbody radiation the relativer components of each color are wel–known, but in other cases, like a fluorescent lamp with visible phosphors, the problem become more complex. You gotta know how much light of each color is present. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [September 21, 2005, 7:37pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/13 "2005-09-21T19:37:41Z")
> [@panamajack](#): > > But all of the power output of an incandescent is in photons. No, some of it will be in the form of heat. Conduction and convection. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [September 21, 2005, 10:43pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/14 "2005-09-21T22:43:08Z")
> [@Chronos](#): > > Almost all of the energy which goes into a bulb comes out as light. It’s just that only a small amount of it is _visible_ light. Most of the energy is in infrared light, which has less energy per photon. Is this true for fluorescent bulbs as well, or just incandescent? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 22, 2005, 4:43am UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/15 "2005-09-22T04:43:19Z")
> [@](#): > > Is this true for fluorescent bulbs as well, or just incandescent? It’ll depend more on the housing, shade, and the like than on the bulb technology itself. Any energy which goes into the bulb will either turn directly into light or into heat (for an incandescent, it’s all into heat). The energy which went into heat will then leave the bulb through one of three mechanisms: Conduction, convection, or radiation. For most light fixtures, radiation would be the dominant form of heat transfer, which would mean that most of the heat energy is leaving via photons (this is in fact the only mechanism by which incandescent bulbs produce photons). What frequencies these photons are produced at will depend on the temperature; for ordinary incandescent bulb temperatures, most of them are infrared. ---
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [September 22, 2005, 5:23am UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/16 "2005-09-22T05:23:36Z")
> [@Chronos](#): > > It’ll depend more on the housing, shade, and the like than on the bulb technology itself. Any energy which goes into the bulb will either turn directly into light or into heat (for an incandescent, it’s all into heat). The energy which went into heat will then leave the bulb through one of three mechanisms: Conduction, convection, or radiation. For most light fixtures, radiation would be the dominant form of heat transfer, which would mean that most of the heat energy is leaving via photons (this is in fact the only mechanism by which incandescent bulbs produce photons). What frequencies these photons are produced at will depend on the temperature; for ordinary incandescent bulb temperatures, most of them are infrared. I’ve looked around some but I haven’t found any data on how much of the heat is convected away. But you are pretty close to right that the majority is radiated in one form or another. Even some of that which is conducted away is emitted as radiation. I’ll withdraw my objection to using power input as a measure of how many photons come from a light bulb. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [September 22, 2005, 1:05pm UTC](https://boards.straightdope.com/t/how-many-photons-emitted-from-a-light-bulb/322736/17 "2005-09-22T13:05:57Z")
Continuing what David Simmons & Chonos were just discussing, the filament gives off almost 100% of it’s energy input as photons. Very little heat gets conducted back into the base of the bulb down the filament supports. Now when those photons hit the frosted glass globe, a bunch of them get absorbed and converted to heat that convects or oonducts. So the answer depends a bunch on whether we’re talking about filament output or bulb output.