A laser produces 20.0 mW of red light. In 1.00 hr , the laser emits 2.29 ×10^20 photons. What is

A laser produces 20.0 mW of red light. In 1.00 hr , the...

Key Concepts

Planck's Constant and the Speed of Light

Planck's constant (h) and the speed of light (c) are fundamental constants in quantum physics. They appear in the photon energy equation E = hc/? and are critical for understanding the quantization of energy and the behavior of electromagnetic radiation. These constants bridge the gap between wave properties and particle properties of light.

Unit Conversion

In many physics problems, it is essential to convert between units of time, power, and energy to maintain consistency in calculations. For example, converting hours to seconds when dealing with power expressed in watts (joules per second) ensures that the units match correctly in the energy calculations.

Power and Energy Relationship

Power is defined as the rate at which energy is transferred or emitted, quantified as energy per unit time. When a system has a given power output, the total energy produced over a time interval can be found by multiplying the power by the duration of time, which is crucial for linking the energy delivered to the number of photons emitted.

Photon Energy

Photon energy is determined by the equation E = hc/?, where h is Planck's constant, c is the speed of light, and ? is the photon's wavelength. This relationship shows that the energy of a photon is inversely proportional to its wavelength, meaning that shorter wavelengths correspond to higher energy photons and vice versa.

Transcript

00:01 Hello, beba, how's it going? for this question, we're given the power of 20 minnow watts, and we know the laser emits a certain number of photons per hour, and we're supposed to find the wavelength.

00:12 The way we're going to do it is we have to simplify or digest the units first.

00:16 We know that a watt is basically 1 joules per 1 second.

00:21 That's the unit for the power of watt, it's energy per time.

00:25 So we know 20 milawatts is going to be 20 -bivableness.

00:30 By 1 ,000 for the mill joules per second.

00:35 Those two are the same thing.

00:36 Now we have joules per second.

00:39 And we know the photons per hour, we can convert it into photons per second.

00:43 So the 2 .29 times 10 to the power of 20 photons per second is going to be this much of photons per 360 seconds, right? that's conversion between second and hour.

01:00 And we're supposed to find a wavelength.

01:02 We can note here that both of those expressions have second, and we can invert this expression here, so the seconds will go up, and the photons will go down, and the seconds can cancel out, leaving only the jewels here, and the photons here, which is going to give us a unit overall of joules per photon.

01:21 That's the unit for energy.

01:24 And we know that we can relate wavelength with energy by the following equation.

01:29 Energy equals to planx constant equals to frequency and we switch on the frequency planx constant times c speed of that in the vacuum developed by lambda right and then we can rearrange the equation in terms of the wavelength so we're getting lambda equals to plank's constant times speed of light in the vacuum divided by the energy in photons per second and now we can use this equation here and this expression and that expression together we can find the wavelength.

02:03 So i'm going to copy down hc divided by e.

02:08 We have planx conson equals to 6 .63 times 10 to the negative to the power of negative 34 joules second and then we have speed of light three times 10 to the power of 8 meters per second and now we have the energy the tricky part.

02:30 So let's incorporate this expression first.

02:32 We have 20 divided by 1 ,000, joules, per one second and this guy here.

02:39 Remember, we have to invert this so that we can cancel out this unit of seconds...

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