Find the energy,the mass and the momentum of a photon of ultraviolet radiation of 280nm wavelength.

To find the energy, mass, and momentum of a photon with a wavelength of 280 nm (nanometers), we can use some fundamental equations from physics. Let's break this down step by step.

Calculating the Energy of the Photon

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

E = h * f

Where:

• E is the energy of the photon (in joules).
• h is Planck's constant, approximately 6.626 x 10^-34 J·s.
• f is the frequency of the photon (in hertz).

First, we need to find the frequency (f) using the relationship between wavelength (λ) and frequency:

f = c / λ

Where:

• c is the speed of light, approximately 3.00 x 10^8 m/s.
• λ is the wavelength in meters. Since 280 nm is equal to 280 x 10^-9 m, we can substitute this value in.

Now, substituting the values:

f = (3.00 x 10^8 m/s) / (280 x 10^-9 m) ≈ 1.07 x 10^{15} Hz

Now that we have the frequency, we can calculate the energy:

E = (6.626 x 10^-34 J·s) * (1.07 x 10^{15} Hz) ≈ 7.09 x 10^-19 J

Determining the Mass of the Photon

Photons are massless particles, which means they do not have rest mass. However, they do have energy and momentum, which can be related to an equivalent mass using Einstein's famous equation:

E = mc²

We can rearrange this to find an equivalent mass:

m = E / c²

Substituting the energy we calculated and the speed of light:

m = (7.09 x 10^-19 J) / (3.00 x 10^8 m/s)² ≈ 7.87 x 10^{-38} kg

Finding the Momentum of the Photon

The momentum (p) of a photon can be calculated using the formula:

p = E / c

Substituting the energy we found earlier:

p = (7.09 x 10^-19 J) / (3.00 x 10^8 m/s) ≈ 2.36 x 10^{-27} kg·m/s

Summary of Results

To summarize our findings:

• Energy of the photon: 7.09 x 10^-19 J
• Equivalent mass of the photon: 7.87 x 10^{-38} kg
• Momentum of the photon: 2.36 x 10^{-27} kg·m/s

This analysis illustrates the fascinating nature of photons, which, despite having no rest mass, carry energy and momentum, allowing them to interact with matter in significant ways. If you have any further questions or need clarification on any part of this process, feel free to ask!