Momentum of Photon Formula with Solved Examples

Momentum Of Photon Formula: Photon momentum is a fundamental concept in various fields of physics, including quantum mechanics, electromagnetism, and optics. It plays a crucial role in phenomena such as the photoelectric effect, radiation pressure, and the behavior of light in various materials. Despite being massless, photons can transfer their momentum to other objects, such as electrons in the photoelectric effect, and they are key to understanding the behavior of electromagnetic waves.

Definition of Photon Momentum

Momentum Of Photon Formula: Photon momentum is the momentum carried by a photon, which is a discrete packet of electromagnetic radiation. It's a fundamental concept in quantum mechanics, as photons exhibit both particle-like and wave-like properties.

Momentum of Photon Formula

The formula to calculate the momentum of a photon is given by:

P = h/λ

Where:

P is the momentum of the photon.

h is Planck's constant (approximately 6.626 x 10 ^{- 34} J·s).

λ is the wavelength of the photon.

Applications of Momentum of Photon Formula

Photon momentum is crucial in the understanding of the photoelectric effect.

It plays a role in radiation pressure and the propulsion of solar sails.

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Solved Examples of Momentum of Photon Formula

Example 1: Calculate the momentum of a photon with a wavelength of 500 nm.

Solution:

Using the formula:

P = h / λ

P = (6.626 x 10^-34 J·s) / (500 x 10^-9 m)

P ≈ 1.325 x 10^-27 kg·m/s

Example 2: A photon has a momentum of 3.0 x 10 ^-27 kg·m/s. Calculate its wavelength.

Solution:

Rearranging the formula:

λ = h / P

λ = (6.626 x 10^-34 J·s) / (3.0 x 10^-27 kg·m/s)

λ ≈ 2.209 x 10^-7 m or 220.9 nm

Certainly, here are five more solved examples related to the momentum of photons:

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Example 3: A photon has a momentum of 4.0 x 10^-28 kg·m/s. Calculate its wavelength.

Solution:

Using the formula:

λ = h / P

λ = (6.626 x 10^-34 J·s) / (4.0 x 10^-28 kg·m/s)

λ ≈ 1.656 x 10^-6 m or 1656 nm

Example 4: A photon with a wavelength of 300 nm is incident on a surface. Calculate its momentum.

Solution:

Using the formula:

P = h / λ

P = (6.626 x 10^-34 J·s) / (300 x 10^-9 m)

P ≈ 2.209 x 10^-27 kg·m/s

Example 5: Two photons, one with a wavelength of 400 nm and the other with a wavelength of 600 nm, collide and scatter in opposite directions. Calculate the total momentum before and after the collision.

Solution:

Before the collision:

P1 = h / λ1

P1 = (6.626 x 10^-34 J·s) / (400 x 10^-9 m)

P1 ≈ 1.656 x 10^-27 kg·m/s

P2 = h / λ2

P2 = (6.626 x 10^-34 J·s) / (600 x 10^-9 m)

P2 ≈ 1.104 x 10^-27 kg·m/s

Total momentum before the collision = P1 - P2 = (1.656 - 1.104) x 10^-27 kg·m/s ≈ 0.552 x 10^-27 kg·m/s

After the collision, the total momentum remains the same as momentum is conserved.

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Example 6: A green laser emits light with a wavelength of 532 nm. Calculate the momentum of each photon in the laser beam.

Solution:

Using the formula:

P = h / λ

P = (6.626 x 10^-34 J·s) / (532 x 10^-9 m)

P ≈ 1.247 x 10^-27 kg·m/s

Example 7: An X-ray photon has a momentum of 1.5 x 10^-24 kg·m/s. Calculate its wavelength.

Solution:

Using the formula:

λ = h / P

λ = (6.626 x 10^-34 J·s) / (1.5 x 10^-24 kg·m/s)

λ ≈ 4.417 x 10^-11 m or 0.04417 nm