Chapter 10: Problem 6

What is a photon? How is its energy related to its frequency? To its wavelength?

Short Answer

Expert verified

The energy of a photon is directly proportional to its frequency (E = h * f) and inversely proportional to its wavelength (E = h * c / λ), where E is the energy, h is Planck's constant, f is the frequency, c is the speed of light, and λ is the wavelength. The higher the frequency or the shorter the wavelength, the higher the energy of the photon.

Step by step solution

Define a Photon

A photon is a discrete packet or quantum of electromagnetic radiation, which carries energy. It has no mass and can typically be represented as a wave or a particle (wave-particle duality). The concept of a photon was introduced by Albert Einstein in 1905 to describe the behavior of electromagnetic radiation such as light.

Provide Background Information

In classical physics, electromagnetic radiation was described as waves with varying energies and frequencies. However, the wave model couldn't explain certain phenomenon such as the photoelectric effect. This led to the development of the concept of quantized energy levels and the birth of quantum physics. Electromagnetic radiation can be quantized into discrete energy levels, and these energy levels are carried by photons.

Planck's Relation

The energy of a photon is directly proportional to its frequency, which can be described by Planck's relation. Planck's relation states that the energy of a photon (E) is the product of Planck's constant (h) and the frequency of the electromagnetic radiation (f). Mathematically, it is represented as: E = h * f, where E is the energy of the photon, h is Planck's constant (approximately 6.626 x 10^{-34} Js), and f is the frequency of the electromagnetic radiation.

Relationship between Energy and Frequency

As mentioned earlier, the energy of a photon is directly proportional to its frequency. The higher the frequency of the electromagnetic radiation, the higher the energy of the photon. Using the aforementioned formula (E = h * f), we can determine the energy of a photon if its frequency is known.

Relationship between Energy and Wavelength

The energy of a photon is also related to its wavelength through the speed of light (c). The speed of light is approximately 3.0 x 10^{8} m/s. The relationship between frequency (f) and wavelength (λ) can be described using the following equation: c = f * λ. From the previous relationship between energy and frequency, E = h * f, and substituting f with c/λ, we obtain E = h * c / λ. Thus, the energy of a photon is inversely proportional to its wavelength: the shorter the wavelength, the higher the energy of the photon and vice versa.

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What is a photon? How is its energy related to its frequency? To its wavelength?

Short Answer

Step by step solution

Define a Photon

Provide Background Information

Planck's Relation

Relationship between Energy and Frequency

Relationship between Energy and Wavelength

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