“Photon energy”的意思、由来-开放百科全书

Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.

Photon energy is solely a function of the photon's wavelength. Other factors, such as the intensity of the radiation, do not affect photon energy. In other words, two photons of light with the same color and therefore, same frequency, will have the same photon energy, even if one was emitted from a wax candle and the other from the Sun.

Photon energy can be represented by any unit of energy. Among the units commonly used to denote photon energy are the electronvolt (eV) and the joule (as well as its multiples, such as the microjoule). As one joule equals 6.24 × 10¹⁸ eV, the larger units may be more useful in denoting the energy of photons with higher frequency and higher energy, such as gamma rays, as opposed to lower energy photons, such as those in the radiofrequency region of the electromagnetic spectrum.

Formula

Where E is photon energy, h is the Planck constant, c is the speed of light in vacuum and λ is the photon's wavelength. As h and c are both constants, photon energy changes in inverse relation to wavelength λ.

To find the photon energy in electronvolts, using the wavelength in micrometres, the equation is approximately

Therefore, the photon energy at 1 μm wavelength, the wavelength of near infrared radiation, is approximately 1.2398 eV.

This equation is known as the Planck-Einstein relation. Substituting h with its value in J⋅s and f with its value in hertz gives the photon energy in joules. Therefore, the photon energy at 1 Hz frequency is 6.62606957 × 10⁻³⁴ joules or 4.135667516 × 10⁻¹⁵ eV.

is used where h is Planck's constant and the Greek letter ν (nu) is the photon's frequency.^[2]

Examples

An FM radio station transmitting at 100 MHz emits photons with an energy of about 4.1357 × 10⁻⁷ eV. This minuscule amount of energy is approximately 8 × 10⁻¹³ times the electron's mass (via mass-energy equivalence).

The highest energy gamma rays detected to date, very-high-energy gamma rays, have photon energies of 100 GeV to 100 TeV (10¹¹ to 10¹⁴ electronvolts) or 16 nanojoules to 16 microjoules. This corresponds to frequencies of 2.42 × 10²⁵ to 2.42 × 10²⁸ Hz.

A photon with a wavelength equal to the Planck length would have an energy of about 7.671 × 10²⁸ eV or 1.229 × 10¹⁰ joules (12.29 gigajoules). This is roughly the amount of energy produced by the world's most powerful coal-fired power station, the Taichung Power Plant, during a period of 2.25 seconds.

During photosynthesis, specific chlorophyll molecules absorb red-light photons at a wavelength of 700 nm in the photosystem I, corresponding to an energy of each photon of ≈ 2 eV ≈ 3 x 10⁻¹⁹ J ≈ 75 k_BT, where k_BT denotes the thermal energy. A minimum of 48 photons is needed for the synthesis of a single glucose molecule from CO₂ and water (chemical potential difference 5 x 10⁻¹⁷ J) with a maximal energy conversion efficiency of 35%.

Formula

Examples

See also

References