Radiant energy

The radiation energy is a physical quantity in radiometry . It is the energy that is transported by electromagnetic waves , for example light , or the energy of electromagnetic waves that is contained in a given area of ​​space and at a defined point in time . The SI unit of radiant energy is the joule .

Radiation intensity of the sun above and on the earth's surface

description

If you consider electromagnetic radiation as a stream of photons , the radiant energy is the energy transported in this stream.

The energy of a photon only depends on the frequency:

${\displaystyle E=h\cdot f}$

with Planck's quantum of action and the frequency of the wave . ${\displaystyle h}$ ${\displaystyle f}$

In the macroscopic area (very many photons) one often uses the symbols or for the radiation energy instead of . For monochromatic electromagnetic radiation, for example for monochromatic (single-colored) light , the radiation energy is the product of the number of photons in the spatial area and the energy of a photon: ${\displaystyle E}$ ${\displaystyle Q}$ ${\displaystyle Q_{\mathrm {e} }}$ ${\displaystyle N}$

${\displaystyle Q_{\mathrm {e} }\equiv E=N\cdot h\cdot f.}$

As a rule, however, electromagnetic radiation consists of photons of different energies. In the case of light, one speaks of polychromatic (multicolored) light . For a general description of the radiation energy one must therefore consider the spectral distribution, which indicates how many photons are in a frequency range from to : ${\displaystyle \mathrm {d} N}$ ${\displaystyle f}$ ${\displaystyle f+\mathrm {d} f}$

${\displaystyle n(f)={\frac {\mathrm {d} N}{\mathrm {d} f}}}$

The following results for the radiation energy:

${\displaystyle Q_{\mathrm {e} }\equiv E=h\int _{0}^{\infty }n(f)\cdot f\ \mathrm {d} f}$,

Connection with other quantities

Radiated power

Looking at the time when a certain amount of radiation energy is transported, there is the radiation power (also called radiant flux) . ${\displaystyle \Phi _{\mathrm {e} }}$ ${\displaystyle \Phi _{\mathrm {e} }={\frac {\mathrm {d} Q_{\mathrm {e} }}{\mathrm {d} t}}}$

Photometry

In photometry , the sensitivity of the human eye is also taken into account, which depends on the frequency or wavelength. The quantity weighted in this way is the amount of light . The indices e and v stand for energetic and visual . ${\displaystyle Q_{\mathrm {v} }}$

Overview

radiometric quantity	Symbol a)	SI unit	description	photometric equivalent b)	symbol	SI unit
Radiant flux radiant power, radiant flux, radiant power	${\displaystyle \Phi _{\mathrm {e} }}$	W ( watt )	Radiant energy through time	Luminous flux luminous flux, luminous power	${\displaystyle \Phi _{\mathrm {v} }}$	lm ( lumens )
Radiant intensity irradiance, radiant intensity	${\displaystyle I_{\mathrm {e} }}$	W / sr	Radiation flux through solid angles	Luminous intensity luminous intensity	${\displaystyle I_{\mathrm {v} }}$	cd = lm / sr ( candela )
Irradiance irradiance	${\displaystyle E_{\mathrm {e} }}$	W / m 2	Radiation flux through the receiver surface	Illuminance illuminance	${\displaystyle E_{\mathrm {v} }}$	lx = lm / m 2 ( lux )
Specific radiation emission current density, radiant exitance	${\displaystyle M_{\mathrm {e} }}$	W / m 2	Radiation flux through the transmitter surface	Specific light emission luminous exitance	${\displaystyle M_{\mathrm {v} }}$	lm / m 2
Radiance radiance, radiance, radiance	${\displaystyle L_{\mathrm {e} }}$	W / m 2 sr	Radiant intensity through effective transmitter area	Luminance luminance	${\displaystyle L_{\mathrm {v} }}$	cd / m 2
Radiant energy amount of radiation, radiant energy	${\displaystyle Q_{\mathrm {e} }}$	J ( joules )	by radiation transmitted energy	Amount of light luminous energy, quantity of light	${\displaystyle Q_{\mathrm {v} }}$	lm · s
Irradiation irradiation, radiant exposure	${\displaystyle H_{\mathrm {e} }}$	J / m 2	Radiant energy through the receiver surface	Exposure luminous exposure	${\displaystyle H_{\mathrm {v} }}$	lx s
Radiation yield radiant efficiency	${\displaystyle \eta _{\mathrm {e} }}$	1	Radiation flux through absorbed (mostly electrical) power	Luminous efficiency (overall) luminous efficacy	${\displaystyle \eta _{\mathrm {v} }}$	lm / W

^a)The index "e" is used to distinguish it from the photometric quantities. It can be omitted.

^b)The photometric quantities are the radiometric quantities, weighted with the photometric radiation equivalent K , which indicates the sensitivity of the human eye.

Individual evidence

1. ↑ Horst Stöcker (editor): Pocket book of physics: formulas, tables, overviews . 6., corr. German edition, Frankfurt am Main 2010, ISBN 978-3-8171-1861-8 , pp. 369 (XXIV, 1079).
2. ↑ Horst Stöcker (editor), ibid, p. 734.