The output power of a laser pointer is about 1 mW. (a) What are the energy and momentum of one

step 1 In this exercise, we're given a laser whose power is 1 mm -watt. And in question 8, we're asked

The output power of a laser pointer is about 1 mW. (a) What...

The output power of a laser pointer is about $1 \mathrm{~mW}$. (a) What are the energy and momentum of one laser photon if the laser wavelength is $670 \mathrm{~nm} ?$ (b) How many photons per second are emitted by the laser? (c) What is the average force on the laser due to the momentum carried away by these photons?

The output power of a laser pointer is about $1 \mathrm{~mW}$.
(a) What are the energy and momentum of one laser photon if the laser wavelength is $670 \mathrm{~nm} ?$ (b) How many photons per second are emitted by the laser?
(c) What is the average force on the laser due to the momentum carried away by these photons?

Key Concepts

Photon Energy

Photon energy is a fundamental concept in quantum mechanics, defined by the relationship E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the photon. This concept connects the quantized energy of light to its wavelength, providing a way to compute the energy carried by individual photons.

Photon Momentum

Photon momentum arises from the wave-particle duality of light and is given by the relation p = E/c, where E is the photon energy and c is the speed of light. Despite having no mass, photons carry momentum, which allows them to exert pressure and impart forces upon interaction with matter.

Laser Power and Photon Emission Rate

Laser power represents the energy output per unit time, and it is related to the number of photons emitted per second. By dividing the laser’s power by the energy per photon, one can determine the rate at which photons are emitted, linking macroscopic power output with microscopic quantum events.

Radiation Pressure and Force

Radiation pressure is the pressure exerted by light due to the momentum carried by photons. When photons are emitted, absorbed, or reflected, their momentum transfer results in a force on the emitting or interacting object. The average force can be computed as the rate of momentum change, illustrating how even low-energy photons can produce measurable forces over time.

Transcript

00:01 In this exercise, we're given a laser whose power is 1 mm -watt.

00:07 And in question 8, we're asked to calculate what is the energy and the momentum of a photon emitted by this laser if the photon has a wavelength of 670 nanometers.

00:22 We know that the energy of a photon is given by hc over lambda.

00:28 Hc is 120 electron volts nanometers.

00:34 Lambda is 670 nanometers.

00:39 So the energy of a single photon is going to be 1 .85 electron volts, which is the same if you multiply it by 1 .6 times 10 to the minus 19 joules per electron volts.

00:52 You're going to have 2 .996 times 10 to the minus, 19 joules.

01:02 For the momentum of a single photon, we get h over lambda.

01:12 H is 6 .63 times 10 to the minus 34 joules second and lambda in meters is 6 .7 times 10 to minus 7 meters so that the momentum is 9 .9 times 10 to minus 28 kilograms meters per second.

01:38 So this is the answer to question a.

01:41 Let's go to question b.

01:43 In question b, we have to calculate what is the number of photons per second that are emitted by this laser.

01:51 So you know that the potency of the laser is 1 milliwatt, which is the same to say that it emits 1 mili jule per second, or 10 to the minus 3 joules.

02:03 Each second.

02:06 Okay.

02:07 So the number of photons per second is going to be the power of the of the laser, laser divided by the energy of a single photon...

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