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

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

Understanding Photon Properties

A photon is a particle of light that carries energy and momentum but has no rest mass. The properties of a photon can be calculated using its wavelength, which in this case is 280 nm (nanometers).

Step 1: Convert Wavelength to Meters

First, we need to convert the wavelength from nanometers to meters since the standard unit for wavelength in physics is meters. Since 1 nm is equal to \(1 \times 10^{-9}\) meters, we can convert:

• 280 nm = \(280 \times 10^{-9}\) m = \(2.8 \times 10^{-7}\) m

Step 2: Calculate the Energy of the Photon

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

E = \frac{hc}{\lambda}

Where:

• h = Planck's constant = \(6.626 \times 10^{-34}\) J·s
• c = speed of light = \(3.00 \times 10^8\) m/s
• \(\lambda\) = wavelength in meters

Substituting the values into the equation:

E = \frac{(6.626 \times 10^{-34} \text{ J·s})(3.00 \times 10^8 \text{ m/s})}{2.8 \times 10^{-7} \text{ m}}

Calculating this gives:

E ≈ 7.1 \times 10^{-19} \text{ J}

Step 3: Determine the Mass of the Photon

Photons are massless particles, meaning they do not have rest mass. However, we can calculate the equivalent mass using Einstein's famous equation:

m = \frac{E}{c^2}

Substituting the energy we found and the speed of light:

m = \frac{7.1 \times 10^{-19} \text{ J}}{(3.00 \times 10^8 \text{ m/s})^2}

Calculating this gives:

m ≈ 7.9 \times 10^{-38} \text{ kg}

Step 4: Calculate the Momentum of the Photon

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

p = \frac{E}{c}

Substituting the energy we calculated:

p = \frac{7.1 \times 10^{-19} \text{ J}}{3.00 \times 10^8 \text{ m/s}}

Calculating this gives:

p ≈ 2.37 \times 10^{-27} \text{ kg·m/s}

Summary of Results

To summarize, for a photon of ultraviolet radiation with a wavelength of 280 nm:

• Energy: \(7.1 \times 10^{-19}\) J
• Mass: \(7.9 \times 10^{-38}\) kg (equivalent mass)
• Momentum: \(2.37 \times 10^{-27}\) kg·m/s

This analysis illustrates how we can derive important properties of photons using fundamental physics equations. If you have any further questions or need clarification on any of the steps, feel free to ask!