A heat lamp produces 17.7 watts of power at a wavelength of 6.5 μm. How many photons are emitted per second? (1 watt = 1 J/s)

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Hey everyone in this example, we need to determine the number of photons emitted from a compact microwave oven that generates 652 watts per second of power With a wavelength of 12.24 cm. And were given the following conversion factor. We should instantly recognize that we're going to convert a wavelength from centimeters to meters. And we want to convert our energy emitted by our microwave from watts into joules per second. So we're going to use that conversion factor starting out with our energy given as 652 watts per second. We're going to multiply by the given conversion factor where we have one jewel equal to one watch. And so what we can do is cancel out our units of watts, leaving us with jewels per second as our final unit. And so this gives us a value of 652 jewels per second. So now that we have energy in the proper format, we can go ahead and recall our formula for energy, which states that energy is going to be plank's constant, multiplied by our speed of light, divided by our wavelength lambda. And we should recall that our wavelength again needs to be in units of meters. So we're going to convert our 12.24 centimeters, which is our wavelength that were given. And again we want to go from centimeters in the denominator, two m in the numerator. So we should recall that our prefix anti tells us we have 10 to the negative second power meters. Now we're able to cancel out units of centimeters leaving us with meters, our final unit for wavelength. And this gives us a value of 0.12 to four m. So now let's go ahead and plug everything into our formula for energy. So this is calculating energy per photon. And what we're going to get is in our unit, in our numerator we have planks constant, which we should recall is 6.626 times 10 to the negative 34th power jewels, times seconds, multiplied by the speed of light, which we recall is three point oh oh times 10 to the eighth Power meters per second. And then in our denominator we're plugging in that wavelength that we converted to meters as .12-4 m. Now we're able to go ahead and cancel out our unit. So we can get rid of meters. We can get rid of inverse seconds with seconds. And we're left with jewels as our final unit of energy here. And this is going to give us a value of 600 or sorry, one point times 10 to the negative 24th power jewels per photon. And so now that we have our energy per photon, we can find our number of photons By taking that total energy that we calculated in joules per second which is 652 jewels per second. And we're going to multiply this by our Energy per photon. So we said that we have 1.624 times 10 to the negative 24th power jewels per photon. And so now that we have jewels in the numerator and denominator, we can go ahead and cancel out jewels, leaving us with photons per second as our final unit. And so this gives us our final answer equal to 4.01 times 10 to the 26 power photons per second that is emitted by our microwave. And this will complete this example as our final answer. So I hope that everything we reviewed was clear. And if you have any questions, please leave them down below. Otherwise, I'll see everyone in the next practice video.

A heat lamp produces 17.7 watts of power at a wavelength of 6.5 μm. How many photons are emitted per second? (1 watt = 1 J/s)

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Key Concepts

Photon Energy

Power and Energy Relationship

Calculating Photon Emission