Explain black body radiation in 700 word.
Answers
Answered by
0
Black-body radiation
Black-body radiation, also termed Planck’s law, determines the intensity of a radiation (Ie) at a wavelength (λ) from the temperature (T) of the emitter, if the latter is a perfect absorber and emitter (black body):
(F3.1.1)Ie(ν,T)=2hν3c−2/{exp[hν/k(B)T]−1}
where h and k(B) are Planck’s and Boltzmann’s constants respectively, and c is the speed of light, while ν = c/λ. Note that if the units of Ie are W m−2 nm−1sr−1, then the unit of λ is nm. The “sr” denotes steradian, the unit of solid angle.
The Sun is very similar to a black body. Despite significant variations of the solar spectrum near the surface due to many atmospheric processes, especially clouds, total solar radiation in space has been found to be fairly constant. For example, at 645 km ASL, the daily average total solar radiation ranged from 1357 to 1362 W m−2, with an average of 1361 W m−2, from March 2003 to July 2012, according to satellite measurements in a recent mission, the Solar Radiation and Climate Experiment (SORCE) in the USA. Long-term satellite measurements in earlier missions recorded a similar value (1360 W m−2). Satellite-observed solar spectrum during the SORCE mission is illustrated (solid line) in Figure 3.1 for X-ray–ultraviolet–visible–infrared wavelengths (0.1–40 nm, 115–2400 nm). For comparison, the theoretical spectrum from Planck’s law is also shown (dashed line) at T = 5750 K. The correlation coefficient between observed spectrum and theoretical curve was 0.96 over the observed range.
In the 220–800 nm range, the theoretical spectrum, denoted as “Planck’s law 1”, does not capture observations well, as shown in Figure 3.2. The observed solar radiation may be fitted against wavelength using the following formula using the least-squares constraint:
(F3.1.2)ln(Ie(λ))=114.7918+0.0092λ−17.0772lnλ−6291.2504/λ
The fitted curve is also shown in Figure 3.2, together with a curve estimated using the formula (F3.1.3), denoted as “Law 2”, which performs better than Planck’s law but worse than the fitted curve:
(F3.1.3)Ie(λ,T)=2hν3c−2/{exp[hν/k(B)T]−1}
It is shown that the fitted curve is closer to observations, especially for wavelengths <400 nm. Of course, formulae (F3.1.2)and (F3.1.3) are only suitable for the observations described above.
Black-body radiation, also termed Planck’s law, determines the intensity of a radiation (Ie) at a wavelength (λ) from the temperature (T) of the emitter, if the latter is a perfect absorber and emitter (black body):
(F3.1.1)Ie(ν,T)=2hν3c−2/{exp[hν/k(B)T]−1}
where h and k(B) are Planck’s and Boltzmann’s constants respectively, and c is the speed of light, while ν = c/λ. Note that if the units of Ie are W m−2 nm−1sr−1, then the unit of λ is nm. The “sr” denotes steradian, the unit of solid angle.
The Sun is very similar to a black body. Despite significant variations of the solar spectrum near the surface due to many atmospheric processes, especially clouds, total solar radiation in space has been found to be fairly constant. For example, at 645 km ASL, the daily average total solar radiation ranged from 1357 to 1362 W m−2, with an average of 1361 W m−2, from March 2003 to July 2012, according to satellite measurements in a recent mission, the Solar Radiation and Climate Experiment (SORCE) in the USA. Long-term satellite measurements in earlier missions recorded a similar value (1360 W m−2). Satellite-observed solar spectrum during the SORCE mission is illustrated (solid line) in Figure 3.1 for X-ray–ultraviolet–visible–infrared wavelengths (0.1–40 nm, 115–2400 nm). For comparison, the theoretical spectrum from Planck’s law is also shown (dashed line) at T = 5750 K. The correlation coefficient between observed spectrum and theoretical curve was 0.96 over the observed range.
In the 220–800 nm range, the theoretical spectrum, denoted as “Planck’s law 1”, does not capture observations well, as shown in Figure 3.2. The observed solar radiation may be fitted against wavelength using the following formula using the least-squares constraint:
(F3.1.2)ln(Ie(λ))=114.7918+0.0092λ−17.0772lnλ−6291.2504/λ
The fitted curve is also shown in Figure 3.2, together with a curve estimated using the formula (F3.1.3), denoted as “Law 2”, which performs better than Planck’s law but worse than the fitted curve:
(F3.1.3)Ie(λ,T)=2hν3c−2/{exp[hν/k(B)T]−1}
It is shown that the fitted curve is closer to observations, especially for wavelengths <400 nm. Of course, formulae (F3.1.2)and (F3.1.3) are only suitable for the observations described above.
omkashyap:
please make me brainliest
Answered by
0
Attachments:
Similar questions