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What is the Momentum of a Photon?
Grade Level:
Class 12
AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics
Definition
What is it?
A photon is a tiny packet of light energy, and even though it has no mass, it still carries momentum. This momentum helps explain how light can push on objects, like how sunlight pushes on space satellites.
Simple Example
Quick Example
Imagine a cricket ball hitting the stumps. The ball has mass and speed, so it has momentum. A photon is like a super-tiny, massless cricket ball of light. When it hits something, it transfers its 'light momentum', just like the cricket ball transfers its momentum.
Worked Example
Step-by-Step
Let's calculate the momentum of a photon of green light. We know its wavelength is about 500 nanometers (500 x 10^-9 meters).
Step 1: Understand the formula for photon momentum: p = h / lambda, where 'p' is momentum, 'h' is Planck's constant (6.626 x 10^-34 J.s), and 'lambda' is the wavelength.
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Step 2: Identify the given values.
h = 6.626 x 10^-34 J.s
lambda = 500 x 10^-9 m
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Step 3: Plug the values into the formula.
p = (6.626 x 10^-34 J.s) / (500 x 10^-9 m)
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Step 4: Perform the division.
p = (6.626 / 500) x (10^-34 / 10^-9) kg.m/s
p = 0.013252 x 10^(-34 - (-9)) kg.m/s
p = 0.013252 x 10^-25 kg.m/s
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Step 5: Express in standard scientific notation.
p = 1.3252 x 10^-27 kg.m/s
Answer: The momentum of a green light photon is approximately 1.3252 x 10^-27 kg.m/s.
Why It Matters
Understanding photon momentum is crucial for developing technologies like solar sails for spacecraft in space technology and designing precise lasers for medicine. Future engineers and scientists working on quantum computing or advanced sensing will use this concept daily.
Common Mistakes
MISTAKE: Thinking photons have zero momentum because they have zero rest mass. | CORRECTION: Photons do have zero rest mass, but they are always moving at the speed of light, and this motion gives them momentum.
MISTAKE: Using the classical momentum formula (p = mv) for photons. | CORRECTION: The classical formula p=mv is for objects with mass. For photons, which are massless, we use p = h / lambda or p = E / c.
MISTAKE: Confusing photon momentum with electron momentum. | CORRECTION: Photons are light particles; electrons are matter particles. Both have momentum, but their calculation and properties are different.
Practice Questions
Try It Yourself
QUESTION: What is the momentum of a photon with a wavelength of 660 nanometers? (Use h = 6.6 x 10^-34 J.s) | ANSWER: 1 x 10^-27 kg.m/s
QUESTION: If a photon has a momentum of 2.2 x 10^-27 kg.m/s, what is its wavelength? (Use h = 6.6 x 10^-34 J.s) | ANSWER: 3 x 10^-7 m or 300 nanometers
QUESTION: A laser pointer emits photons with a wavelength of 632.8 nm. If each photon has an energy of 3.14 x 10^-19 J, calculate the momentum of one such photon using the energy-momentum relation (p = E/c, where c = 3 x 10^8 m/s). Then, verify this using the Planck's constant formula (p = h/lambda). | ANSWER: Both methods should give approximately 1.047 x 10^-27 kg.m/s
MCQ
Quick Quiz
Which of the following statements about the momentum of a photon is correct?
Photons have no momentum because they have no mass.
Photons have momentum which depends on their wavelength.
Photon momentum can be calculated using p = mv.
Photon momentum is always zero.
The Correct Answer Is:
B
Photons, despite being massless, carry momentum. This momentum is inversely proportional to their wavelength, meaning shorter wavelengths (like blue light) have more momentum than longer wavelengths (like red light).
Real World Connection
In the Real World
ISRO scientists working on advanced propulsion systems are exploring 'solar sails' for spacecraft. These sails are pushed by the momentum of countless photons from the Sun, allowing spacecraft to travel through space without needing fuel. This concept is a direct application of photon momentum.
Key Vocabulary
Key Terms
PHOTON: A tiny packet or quantum of light energy, with no mass. | WAVELENGTH: The distance between two consecutive crests or troughs of a wave. | PLANCK'S CONSTANT (h): A fundamental constant in quantum physics relating energy to frequency and momentum to wavelength. | MOMENTUM: A measure of the 'quantity of motion' of an object, calculated as mass times velocity (for massive objects) or h/lambda (for photons).
What's Next
What to Learn Next
Now that you understand photon momentum, you can explore the 'photoelectric effect'. This concept will show you how light (photons) can knock electrons out of metals, which is key to how solar panels work and will deepen your understanding of light's particle nature.
