Photon Momentum (Micro Lesson for AP Physics)
Summary
TLDRIn this humorous physics lesson, the instructor starts with a light-hearted joke about light having mass, which leads to a deeper discussion on the properties of light. The confusion arises from the common formula P = mv, which doesn't apply to light since it's massless. The instructor clarifies that special relativity allows massless objects like light to have momentum through a loophole. The correct formula to calculate the momentum of a photon is given by P = h/λ, where h is Planck's constant and λ is the wavelength of light in meters. The lesson concludes with the reminder that while a single photon's momentum is minuscule, it can theoretically propel a solar sail, emphasizing the importance of understanding the correct physics behind light's behavior.
Takeaways
- 😀 Light has momentum despite having no mass.
- 😀 The joke about light not being Catholic confused students about light's properties.
- 😀 Light having momentum seems contradictory to the equation P = MV.
- 😀 For objects traveling close to the speed of light, special relativity must be used.
- 😀 Special relativity allows massless objects like photons to have momentum.
- 😀 The formula for photon momentum is H over lambda.
- 😀 H represents Planck's constant (6.626 x 10^-34 joule-seconds).
- 😀 Lambda is the wavelength of light in meters (conversion from nanometers is necessary).
- 😀 The momentum of a single photon is extremely small, hence we don't feel light's push.
- 😀 A large solar sail can be propelled by light due to the impulse from photon momentum.
Q & A
What is the main topic of the physics joke shared in the transcript?
-The main topic of the physics joke is the concept of light having mass, which is humorously refuted by the teacher, only to later explain that light does have momentum without mass.
Why did the teacher's joke confuse the students?
-The joke confused the students because it contradicted their understanding that light has momentum, which they believed implied that light also has mass.
What is the correct formula to determine the momentum of a photon?
-The correct formula to determine the momentum of a photon is momentum equals Planck's constant (H) divided by the wavelength (lambda) of the light, expressed as p = h / λ.
Why is the classical formula P = mv not accurate for calculating the momentum of a photon?
-The classical formula P = mv is not accurate for a photon because it assumes a mass (m) that a photon does not possess. For objects moving at or near the speed of light, special relativity must be considered, which allows for massless objects to have momentum.
What is the significance of the term 'special relativity' in the context of the script?
-Special relativity is significant because it provides a theoretical framework that allows for the possibility of massless particles, like photons, to have momentum, which would otherwise be impossible under classical physics.
Why does the teacher say that light having momentum is a 'loophole'?
-The teacher refers to it as a 'loophole' because, according to classical mechanics, a massless object cannot have momentum. However, special relativity provides an exception to this rule, allowing light, which is massless, to possess momentum.
What is Planck's constant and what is its value?
-Planck's constant (H) is a fundamental physical constant that describes the scale of quantum effects. Its value is approximately 6.6 x 10^-34 joule-seconds.
Why is the momentum of a single photon considered to be extremely small?
-The momentum of a single photon is extremely small because Planck's constant is very small, and the wavelength of visible light is relatively large. This results in a very small value when calculating momentum using the formula p = h / λ.
What is a solar sail and how could it be propelled by light?
-A solar sail is a proposed method of spacecraft propulsion that uses the pressure exerted by the momentum of photons from the Sun to propel a sail. The momentum of light bouncing off the sail could theoretically propel it forward.
Why doesn't the pressure we feel when light shines on us indicate a significant momentum transfer?
-The pressure we feel from light shining on us is minimal because the momentum of individual photons is extremely small. The collective effect of a vast number of photons is required to produce a noticeable force.
What is the importance of converting nanometers to meters when using the formula for photon momentum?
-Converting nanometers to meters is important because the formula for photon momentum uses the wavelength in meters. Wavelengths are often given in nanometers in many contexts, but for the calculation, the correct unit is essential to avoid errors.
How does the concept of momentum in the context of light relate to the broader understanding of quantum mechanics?
-The concept of momentum in the context of light is a fundamental aspect of quantum mechanics, as it demonstrates the dual wave-particle nature of light. Understanding that light can have momentum without mass is a key insight into the principles of quantum theory.
Outlines
🤣 Confusing Physics Joke
The narrator starts by sharing an experience from teaching physics in California, where a joke about light having mass backfired, confusing students. The joke was meant to play on the word 'mass' and religion, but it led to a deeper discussion on whether light actually has mass, given that light has momentum.
📚 Explaining Momentum and Mass of Light
The confusion arises from students understanding that light has momentum and equating that to mass using the equation P = MV. The narrator explains that this equation isn't accurate for objects traveling at the speed of light, such as photons, and introduces the concept of special relativity, which allows massless objects to have momentum.
✨ Special Relativity and Photon Momentum
Special relativity provides a loophole for massless objects like photons to have momentum. The narrator explains that the common formula for momentum (P = MV) is not applicable for photons. Instead, the correct formula is momentum (P) equals Planck's constant (H) divided by the wavelength (λ) of the light.
🔬 Formula for Photon Momentum
The momentum of a photon is given by the formula P = H/λ, where H is Planck's constant (6.626 × 10^-34 joule-seconds) and λ is the wavelength of light in meters. The narrator cautions against using nanometers and highlights that the momentum of individual photons is extremely small, but cumulative effects, such as with a solar sail, can be significant.
🚀 Solar Sail Propulsion
The narrator concludes by emphasizing the practical application of photon momentum, such as using a large solar sail for propulsion in space. Light's momentum can impart an impulse that could move the sail forward, demonstrating the principle that, despite their tiny momentum, photons can exert a measurable force over large surfaces.
📏 Key Takeaway: Proper Formula Usage
The narrator stresses the importance of using the correct formula for calculating the momentum of photons. Instead of using P = MV, one should always use P = H/λ to avoid misunderstandings and inaccuracies in physics calculations involving light.
Mindmap
Keywords
💡Light
💡Mass
💡Momentum
💡Photon
💡Special Relativity
💡Planck's Constant
💡Wavelength (λ)
💡Solar Sail
💡Impulse
💡P = MV
Highlights
Physics teacher in California shares a physics joke in class.
Joke about light holding mass and the confusion it caused.
Students knew that light has momentum.
Clarification that light does have momentum but no mass.
Explanation of P = MV and its limitation for light.
Special relativity allows massless objects like photons to have momentum.
P = MV is not accurate for objects traveling at the speed of light.
Formula for momentum of a photon is P = H / λ.
Planck's constant (H) is 6.626 x 10^-34 joule-seconds.
Lambda (λ) is the wavelength of light in meters.
The momentum of a single photon is extremely small.
Solar sails can be propelled by the momentum of light.
Light bouncing off a large solar sail could propel it forward.
Never use P = MV to find the momentum of a photon.
Always use the formula P = H / λ for the momentum of a photon.
Transcripts
a while back I was teaching physics in
California I got to class and I was all
like hey class you want to hear a
physics joke yeah okay totally does
light hold mass I don't know it does it
no it's not even Catholic oh man she
went to the beach it is really totally
lame but wait doesn't light really have
mass it should
it's called momentum so it's gotta have
mass it adds momentum so it must have
mass whoa hey everyone just calm the
heck down you see the worst part of all
this wasn't that my joke bombed it was
that I actually managed to confuse
people by telling it my students had
read that light has momentum and they
were right light really does have
momentum but then I come to class and
I'm all like hey guess what light has no
mass now my students are thinking to
themselves dude but P equals MV in other
words if momentum equals mass times
velocity how could light which has no
mass ever have momentum well I had to
break it to my students that P equals MV
isn't really accurate for things that
travel close to the speed of life for
things going that fast you have to use
special relativity I don't want to waste
a lot of time talking about special
relativity in this video so you're just
gonna have to take my word for it that
the rules of special relativity allow
for a loophole this loophole provides a
way for massless objects to have
momentum all right so the bad news is
that we cannot use P equals mV
to find the momentum of a photon the
good news is that the formula for the
momentum of a photon is simple the
momentum of a photon equals H over
lambda H is Planck's constant 6.6 to 6
times 10 to the negative 34
joule-seconds lambda is the wavelength
of the light in meters be careful don't
use nanometers you have to convert to
meters
the momentum of a single photon is going
to be extremely small that's why it
doesn't feel like we're getting pushed
on very much when light shines on us
but theoretically if you had a big
enough solar sail the light bouncing off
of that solar sail could propel it
forward due to the impulse imparted by
the momentum of the light okay so very
long story short you should never ever
use P equals MV to find the momentum of
a photon to find the momentum of a
photon you should always use momentum
equals H over lambda
Посмотреть больше похожих видео
5.0 / 5 (0 votes)