Understanding Electron and Photon Momentum

Electromagnetic radiation, including photons, and material particles, like electrons, have momentum. This concept can be illustrated by calculating the velocity of an electron that has the same momentum as a photon with a specific wavelength. In this article, we will explore the process of determining the velocity of an electron when its momentum matches that of a photon with a wavelength of 6045 Angstroms.

Photon Momentum Calculation

First, we begin by examining the photon. The wavelength (λ) of the photon is given as 6045 Angstroms (which is 6045 x 10-10 meters).

The energy (E) of a photon can be calculated using the formula:

E (hc) / λ

And the momentum (p) of the photon can be determined by:

p E / c (h / λ)

Where h is Planck's constant (6.626 x 10-34 Js) and c is the speed of light (3 x 108 m/s).

Now, let's substitute the given values:

p 6.626 x 10-34 / (6045 x 10-10)

Approximate the value:

p ≈ 1.1 x 10-26 kg?m/s

Electron Momentum Matching Photon Momentum

For an electron to have the same momentum as the above-photon, we use the formula for momentum:

Pelectron me v

Where me is the mass of the electron (9.1 x 10-31 kg) and v is the velocity of the electron.

Rearrange the formula to solve for velocity (v):

v Pelectron / me

Substitute the known values:

v (1.1 x 10-26) / (9.1 x 10-31)

Calculate the velocity:

v ≈ 1.2 x 104 m/s

Conclusion and Discussion

In conclusion, the velocity of an electron with the same momentum as a photon of 6045 Angstroms is approximately 12,000 m/s. This calculation provides insight into the behavior of quantum particles at a fundamental level.

Understanding the momentum and velocity of subatomic particles is essential for advancing our knowledge in various fields, including quantum mechanics and particle physics. This application of wave-particle duality helps physicists bridge the gap between classical and quantum physics.