Photon of frequency ? has a momentum associated with it. If c is the velocity of light, the momentum is ?

To understand the momentum of a photon, we first need to recognize that photons are massless particles that travel at the speed of light, denoted as "c." The relationship between a photon's frequency and its momentum is rooted in quantum mechanics and can be expressed through a couple of fundamental equations.

Photon Frequency and Energy

The energy (E) of a photon is directly related to its frequency (ν) by the equation:

E = hν

Here, "h" represents Planck's constant, approximately equal to 6.626 x 10^-34 Joule seconds. This equation tells us that the energy of a photon increases with its frequency.

Momentum of a Photon

Now, when it comes to momentum (p), for a photon, the relationship is given by the equation:

p = E/c

Since we already established that the energy of the photon is E = hν, we can substitute this into the momentum equation:

p = hν/c

Understanding the Variables

• p: Momentum of the photon.
• h: Planck's constant.
• ν: Frequency of the photon.
• c: Speed of light in a vacuum, approximately 3 x 10^8 m/s.

Putting It All Together

So, if you know the frequency of the photon, you can easily calculate its momentum using the formula:

p = (hν)/c

This means that the momentum of a photon is directly proportional to its frequency. Higher frequency photons, like gamma rays, have greater momentum compared to lower frequency photons, such as radio waves.

Example Calculation

Let’s say we have a photon with a frequency of 5 x 10^14 Hz (which is in the visible light spectrum). To find its momentum:

1. Calculate the energy: E = hν = (6.626 x 10^-34 J·s)(5 x 10^14 Hz) = 3.313 x 10^-19 J
2. Now, calculate the momentum: p = E/c = (3.313 x 10^-19 J)/(3 x 10^8 m/s) = 1.104 x 10^-27 kg·m/s

This example illustrates how you can derive the momentum of a photon from its frequency using fundamental constants and relationships in physics. Understanding these concepts not only helps in grasping the behavior of light but also lays the groundwork for more advanced topics in quantum mechanics and particle physics.