Photon Momentum (Micro Lesson for AP Physics)

We Are Showboat

17 Mar 201302:54

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

00:00

🤣 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

Light is electromagnetic radiation that is visible to the human eye. In the video, light is discussed in terms of its physical properties, such as having momentum despite having no mass, which is a concept that confuses the students.

💡Mass

Mass refers to the amount of matter in an object. The video's joke hinges on the confusion between 'mass' as a physical property and the religious mass, and it explores how light can have momentum without having mass.

💡Momentum

Momentum is the product of an object's mass and velocity. In classical mechanics, it is expressed as P = MV. However, the video clarifies that this formula does not apply to light, and instead, the momentum of a photon is calculated using a different formula.

💡Photon

A photon is a quantum of light or other electromagnetic radiation. The video explains that although photons are massless, they still possess momentum, which is crucial for understanding concepts like solar sails.

💡Special Relativity

Special relativity is a theory by Albert Einstein that describes the physics of moving bodies at speeds close to the speed of light. The video touches on special relativity to explain how light can have momentum despite lacking mass.

💡Planck's Constant

Planck's constant (H) is a fundamental constant in quantum mechanics, approximately 6.626 x 10^-34 joule-seconds. It is used in the formula to calculate the momentum of photons, as mentioned in the video.

💡Wavelength (λ)

Wavelength is the distance between successive crests of a wave. In the video, the wavelength (lambda) of light is used in the formula to calculate the momentum of photons, emphasizing the need to convert nanometers to meters.

💡Solar Sail

A solar sail is a spacecraft propulsion method that uses the momentum of light to move. The video references solar sails to illustrate how light's momentum, though small, can be harnessed to propel objects in space.

💡Impulse

Impulse is the change in momentum resulting from a force applied over a period of time. The video discusses how light imparts impulse to objects like a solar sail, causing it to move.

💡P = MV

P = MV is the classical formula for momentum, where P is momentum, M is mass, and V is velocity. The video stresses that this formula does not apply to light, which follows the formula P = H/λ instead.

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.