calculate the mass of a photon with wavelength 5893 angstrom units

To find the mass of a photon based on its wavelength, we can use the relationship between energy, wavelength, and mass. Although photons are massless particles, we can calculate their equivalent mass using Einstein's famous equation, E=mc², where E is energy, m is mass, and c is the speed of light. Let's break this down step by step.

Step 1: Convert Wavelength to Meters

The wavelength you provided is 5893 angstroms. First, we need to convert this to meters since the standard unit of measurement in physics is the meter. One angstrom is equal to 1 x 10^-10 meters.

• 5893 angstroms = 5893 x 10^-10 meters
• 5893 angstroms = 5.893 x 10^-7 meters

Step 2: Calculate the Energy of the Photon

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

E = \frac{hc}{\lambda}

Where:

• E is the energy in joules
• h is Planck's constant (6.626 x 10^-34 J·s)
• c is the speed of light (approximately 3.00 x 10⁸ m/s)
• λ is the wavelength in meters

Substituting the values:

E = (6.626 x 10^-34 J·s) x (3.00 x 10⁸ m/s) / (5.893 x 10^-7 m)

Calculating this gives:

E ≈ 3.37 x 10^-19 joules

Step 3: Relate Energy to Mass

Now that we have the energy, we can find the equivalent mass using the rearranged form of Einstein's equation:

m = \frac{E}{c²}

Substituting the values we have:

m = (3.37 x 10^-19 J) / (3.00 x 10⁸ m/s)²

Calculating this gives:

m ≈ 3.74 x 10^-38 kg

Understanding the Result

This result shows that while photons are massless in the traditional sense, they do have an equivalent mass when considering their energy. This concept is crucial in understanding how light behaves in various physical contexts, such as in gravitational fields or when interacting with matter.

In summary, the equivalent mass of a photon with a wavelength of 5893 angstroms is approximately 3.74 x 10^-38 kg. This illustrates the fascinating interplay between energy and mass in the realm of quantum physics.