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Black Body emissionBlack Body Radiation Spectroscopy

Lodovico Lappetito

Sommario

Black Body Radiation........................................................................................................................................3

Diffraction Grating Spectrometer.....................................................................................................................4

Calculation of the Lamp Filament Temperature...............................................................................................5

Halogen Lamp Spectra at Increasing Temperatures.........................................................................................6

Spectrum of the Sun.........................................................................................................................................8

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Black Body Radiation

In physics a black body is an ideal object that absorbs all incident electromagnetic radiation without reflecting (and is therefore called black according to the classical interpretation of the color of the body).Not reflecting, the black body absorbs all the incident energy and therefore, for energy conservation, re- radiates the whole amount of absorbed energy (emission coefficient equal to that of absorption and equal to one) and therefore has its name solely to the absence of reflection.The radiation emitted by a black body is called black body radiation and the energy density radiated black body spectrum . The spectrum (intensity or density of the emitted radiation as a function of wavelength or frequency) of a black body is a spectrum from the characteristic bell shape (more or less asymmetrical and more or less flattened) solely dependent on its temperature T and not from the matter composing it.The difference between the spectrum of a real object (for example the sun) and an ideal black body allows to identify the chemical composition of that object (in the case of the sun, hydrogen and helium) . This analysis is conducted as part of spectroscopy .

as mentioned above, a black body is an ideal radiator, emitting the greatest possible flow per unit area, for each wavelength for any given temperature. A blackbody also absorbs all radiant energy incident on it : that no energy is reflected or transmitted. The real bodies instead deviate more or less significantly by this definition and are therefore called gray bodies. In other words we can say that all the actual bodies behave more or less as bodies blacks without their reflectivity and transmittance being actually gray bodies.

The intensity distribution of the radiation of a black body at temperature T is given by Planck's radiation law.The wavelength at which the intensity of the radiation emitted by the black body is maximum is given by Wien's Law :

and the total power emitted per unit area (precisely , the intensity) is given by the Stefan- Boltzmann :

with

Both these laws can be inferred from the Planck radiation law, the first by searching for the maximum in terms of the wavelength, the second integrating over all frequencies and the angle solid.

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Diffraction Grating Spectrometer

Inside view with collimating lens, grating and webcam

Detail of the micrometric slit and the spectrometer assembled

Spectrometer Design :

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Webcam Grating

Lens

Slit

Slit

Webcam Grating

Lens

Webcam Lens

Calculation of the Lamp Filament Temperature

As an approximation of a "black body" a 24V halogen bulb was used. The bulb was powered at voltages ranging from 0 to 25V. For each used voltage value the current was measured so as to obtain the resistance of the filament and hence its temperature, the emission spectrum was also acquired with the self-built grating spectrometer.

In incandescent lamps, including halogen lamps, visible radiation is produced by making the filament incandescent with the heat generated by Joule effect with electric current. For a metallic conductor the electrical resistance value varies with temperature according to the relation (approximate but valid in a wide temperature range) :

RT=R0 ⌊1+α (T−T 0 ) ⌋

T0 room temperature that is 300°K T filament temperature α temperature coefficient. For the tungsten, which is the main element of the incandescent lamp

filament, the average value of α is 4.5x10-3.

Therefore, by measuring the resistance value at room temperature R0, for example with an ohmmeter (multimeter), and calculating RT, from the measurement of the potential difference and electric current intensity of the lamp on ( RT = V / I ) , we can obtain the temperature T of the filament.

Voltage (V) Current (A) R (ohm) Temperature °K0 0.00 1.30 300

3.5 0.83 4.22 7995 0.98 5.10 950

7.5 1.18 6.36 116410 1.36 7.35 133515 1.66 9.04 162220 1.94 10.31 184025 2.20 11.36 2020

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Halogen Lamp Spectra at Increasing Temperatures

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T = 799 °K

T = 950 °K

T = 1164 °K

T = 1335 °K

T = 1622 °K

The Webcam Spectrometer has important limitations due to the nonlinear behavior of the webcam and due to the fact that it easily go in saturation. The spectra are for illustration only and may give only qualitative information on the shape of the spectrum. In particular the intensity of the measured radiation cannot be considered a reliable data.

Despite these limitations it is evident the bell shaped curve and the displacement of the emission toward shorter wavelengths when the temperature of the filament is increased, according to Planck's and Wien law.

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T = 1840 °K

T = 2020 °K

Spectrum of the Sun

Sun Spectra

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H2O Atm

O2 Atm

O2 Atm

Hα

Na

Mg Fe

Hγ Hβ

Peak emission at around 530nm => Thus T = 5500Ko (black body radiation / Wien law)Presence of UV (<400nm) and IR (>750nm)

Evidence of the following absorption bands / lines : Atmospheric oxygen absorption band O2 760nm – Fraunhofer A Atmospheric water vapor absorption band 720nm Atmospheric oxygen absorption band O2 684nm – Fraunhofer B Absorption Hα 657nm (Balmer series) Fraunhofer C Absorption Hβ 480nm (Balmer series) Fraunhofer F Absorption Hγ 430nm (Balmer series) Fraunhofer G Sodium absorption line at 589nm Fraunhofer D Iron absorption line at 530nm Fraunhofer E Magnesium absorption line at 520nm Fraunhofer b

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