Photon energy and momentum paradox

In summary, to find the momentum and energy of photons of light with a wavelength of 500nm, you can use the equations momentum = h/wavelength and energy = hf. Using the given values of h = 6.63 x 10^-34 and c = 3.0 x 10^8 ms^-1, the momentum is calculated to be 1.326 x 10^-27 kgms^-1 and the energy is 3.96 x 10^-19 J. However, an alternative method of using the equation p = mv results in a lower energy of 1.99 x 10^-19 J, which is half the value obtained using the first method. This is because the equation p =
  • #1
monstersaurou
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Homework Statement


Find the momentum and energy of photons of light of wavelength 500nm. Usual data of h = 6.63 x 10-34 and c = 3.0 x 108ms-1

Homework Equations


The Attempt at a Solution


> To get momentum, i simply take momentum = h/wavelength = 1.326 x 10-27 kgms-1

> To get energy I use E = hf = 3.96 x 10-19 J

> However, i figured that an alternative way to get energy will be to use the equation p = mv. Since i have already calculated the momentum of my photon in the first step, and I know that the velocity of a photon is 3.0 x 108 ms-1, the mass of the photon will be 4.42 x 10-36 kg. With this mass in mind, I can now use KE = 0.5mv2 (m = 4.42 x 10-36, v = 3.0 x 108 ms-1). Eventually, i obtain a KE of 1.99 x 10-19 J.

> So there is now this paradox that E=hf gives me energy as 3.96 x 10-19 J, while the alternative method gives me energy of 1.99 x 10-19 J, which is half that of the former. I am pretty sure I am missing out on something here. Any idea? Thanks!
 
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  • #2
monstersaurou said:
However, i figured that an alternative way to get energy will be to use the equation p = mv.
The equation p = mv only applies to particles moving slowly compared to light speed. It certainly doesn't apply to photons, which have m = 0.
 

1. What is the photon energy and momentum paradox?

The photon energy and momentum paradox refers to the seemingly contradictory nature of photons having both energy and momentum, yet being massless particles. This paradox arises from the principles of special relativity, which state that the energy and momentum of a particle are related to its mass. Since photons have no mass, it is difficult to reconcile how they can have both energy and momentum.

2. How do photons have energy if they are massless?

According to Einstein's famous equation E=mc², energy and mass are equivalent. This means that even though photons have no rest mass, they still have energy in the form of their electromagnetic wave properties. The energy of a photon is directly proportional to its frequency, or inversely proportional to its wavelength.

3. How is momentum defined for a massless particle like a photon?

Momentum is defined as the product of an object's mass and velocity. Since photons have no mass, their momentum is simply the product of their speed and a quantity known as their relativistic mass. This relativistic mass is dependent on the energy of the photon, and as a result, the momentum of a photon is directly proportional to its energy.

4. Can the photon energy and momentum paradox be resolved?

Yes, the paradox can be resolved by understanding that the principles of special relativity apply differently to massless particles like photons. In this case, the relationship between energy, momentum, and mass is described by the famous equation E²=(pc)²+(mc²)², where p is the momentum of the photon, c is the speed of light, and m is the relativistic mass. This equation shows that even though photons have no mass, they still have energy and momentum that are related to each other.

5. Why is the photon energy and momentum paradox important?

The photon energy and momentum paradox is important because it helps us understand the fundamental properties of particles and the principles of special relativity. It also has practical applications in fields such as quantum mechanics and astrophysics, where the behavior of photons is crucial to understanding the behavior of matter and energy in the universe.

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