The kinetic mass of a photon is calculated using the formula m = h / (λc) where h is Planck's constant, λ is the photon's wavelength, and c is the speed of light.
Here's a breakdown:
- Planck's Constant (h): A fundamental constant in quantum mechanics, approximately 6.626 x 10-34 joule-seconds. It relates a photon's energy to its frequency.
- Wavelength (λ): The distance between successive crests of a wave, usually measured in meters. The wavelength of a photon determines its position on the electromagnetic spectrum.
- Speed of Light (c): The speed at which light travels in a vacuum, approximately 3 x 108 meters per second.
Calculation:
The reference provided, "kinetic mass of photon=m=hcλ," seems incorrect; it should be m = h / (λc). The formula given shows the kinetic mass, m, being calculated as h (Planck's Constant) multiplied by the speed of light, c, multiplied by the wavelength of the photon, λ, which gives an incorrect result. The correct relation between the energy of a photon E=mc2 and E=hc/λ leads to m=h/cλ.
Here is the correct formula again:
m = h / (λc)
This formula is derived from the following concepts:
- Energy of a photon: E = h * f, where f is the frequency.
- Relationship between frequency and wavelength: f = c / λ
- Einstein's mass-energy equivalence: E = mc2
By substituting the second and third equations into the first, and rearranging, we obtain:
hc/λ = mc2
m = h/(λc)
Understanding Kinetic Mass:
- Photons, being massless particles, do not possess rest mass. Instead, they have kinetic mass, which is related to their energy of motion.
- The shorter a photon's wavelength (higher frequency and energy), the greater its kinetic mass, and vice versa.
- The kinetic mass is always present for moving photons as they have momentum.
Example:
Let's take a photon with a wavelength of 500 nanometers (500 x 10-9 m), which corresponds to green light:
- Planck's constant (h): 6.626 x 10-34 J⋅s
- Speed of light (c): 3 x 108 m/s
- Wavelength (λ): 500 x 10-9 m
m = (6.626 x 10-34 J⋅s) / [(500 x 10-9 m) x (3 x 108 m/s)]
m ≈ 4.417 × 10-36 kg
This example illustrates how small the kinetic mass of a photon is.
| Parameter | Value |
|---|---|
| Planck's Constant (h) | 6.626 x 10-34 J⋅s |
| Speed of Light (c) | 3 x 108 m/s |
| Wavelength (λ) | Varies, depends on photon |
| Kinetic Mass (m) | m = h / (λc) |
