On an Experiment of Black Body Radiation - Lab Report Example

Running Head: LAB REPORT on an EXPERIMENT of BLACK BODY RADIATION Lab Report on an Experiment of Black Body Radiation Name Institution Black Body Radiation Abstract Materials that emit or absorb all the energy that has been directed to them are usually referred to as black bodies and they all behave identically. In this experiment substances were heated to test their emission of electromagnetic radiation over a range of wavelengths. In most cases different materials always display differences when it comes to spectral distribution of their radiations. This is because each material emits or absorbs radiation differently. In the end the results derived from this experiment were to be used to understand the Planck’s equation more clearly and to learn its applications in real life situations. The experiment was also carried out for the purposes of measuring the ratio of the f\fundamental physics constants by measuring the radiation that had been emitted by a heated tungsten wire. Another use of this experiment was to learn on methods of instrumentation and other techniques by measuring high temperatures using an optical pyrometer. The techniques were also made more clear learning on the calibration of a direct reading wavelength spectrometer and what it is used for in the measuring of intensities in light. Introduction In physics an object is referred to as a black body if it has the ability to absorb all the electromagnetic radiation that happens to fall on it. They absorb and also emit radiation in a specific manner and also in a spectrum that is continuous. The emitted radiation is not usually depended on the type of radiation that fell on it. Therefore the radiated energy can be said to have been produced a standing wave or by some resonant modes of cavity that are radiating (Baggott, 2004). During the emission of radiation by black bodies no light is transmitted therefore the object will always appear black when cold. Black body radiation is a term coined from the fact that a black body emits a radiation that is depended on temperature. Therefore this thermal radiation that is emitted by a black body is what is called the black body radiation. In this spectrum of radiation emitted by the black body, there are both short and longer wavelengths. The shorter the wavelength the higher the frequency and this high frequency causes high temperature. A good example of a black body radiation is a furnace. Heat energy can enter from the outside to the furnace if there happens to be an opening at the door. If this happens, this outside heat is absorbed by the walls of the furnace on the inside. The walls on the other hand are also very hot and therefore also emitting radiation which in turn can be absorbed by another part of the furnace or it could also escape through the opening at the door. This therefore makes the furnace to be at some kind of equilibrium. Why do heated bodies radiate? How is this radiation absorbed? To answer the first question we have to understand the mechanisms involved. Heat is known to cause molecules and atoms to vibrate. These molecules and atoms are made up of complicated patterns of electrical charges. Therefore when a body is heated their molecules and atoms vibrate and consequently these vibrations cause charge oscillations, these oscillations on the other hand radiate giving out heat and light. To understand how this radiation is absorbed we have understand what is meant by the word black body radiation (Greiner, 2001). To some extend the radiation given out by a heated body depends on the body being heated. Different objects absorb radiation differently some do not seem to absorb radiation at all like glass. These objects show that much difference when it comes to radiation absorption because there are charges in different objects that can oscillate to respond to an oscillating electric field applied externally. Apparatus Optical pyrometer (Leeds and Northrup Model 8627) GRD7 Thermionic Diode and associated power supply Direct Reading Wavelength Spectrometer Thorlabs Photodetector, Digital Multimeters, Mercury Spectral Lamp Procedure The GRD7’s tungsten filament was used as the emitting surface. The apparent temperature of the filament was determined as a function of a heating current by the use of the optical pyrometer. The spectrometer calibration was checked before measuring the light intensity emitted by the filament. The properties of the spectrometer were also considered. These properties are used to determine the wavelength band which is passed to the light detector. Measurements of ITas a function of T were made for at least two wavelengths and the quantity hc/k was obtained from the experimental results recorded. Calibration of Filament Temperature The pyrometer was used to obtain a calibration table relating the GRD7 filament current to the apparent temperature of the black box. The filament was observed through a hole in the central anode. The filament’s current was observed and monitored in the range 1.7- 2.2. Temperature measurements were made at each current setting so as to obtain an estimate of reliable results. Calibrating the Spectrometer The spectrometer was set up and the mercury spectrum examined. The calibration was also checked against the mercury spectrum’s standard lines and adjusted appropriately using the green line. Slit Widths of the Spectrometer The effect of the source slit and the width of the detector slit width on the band- pass characteristics of the spectrometer were investigated using the mercury spectrum. The source slit was set up so that it could pass a bandwidth of 10nm and then the blades were also set to form the detector slit to pass the same bandwidth of 10nm. Setting up the Detector The photo cathodes used for releasing photoelectrons, the dynodes used for multiplying the electrons produced and the anode used for collecting the current pulse are the three most important elements of a photomultiplier tube. Each of these elements must be placed at a successfully higher potential for the electrons to pass from the dynodes to the anodes for their successful collection. For the experiment a Thorlabs solid state detector was used. The eyepiece was removed and replaced with the said detector. The detector’s output voltage was monitored using a DMM. Measuring of the Intensities] The Hg lamp was removed and the GRD7 set up so that the cathode wire was parallel to the slit of the spectrometer. The spectrum was placed centrally and the eyepiece replaced with the photo detector. The position of the GRD7 was adjusted so as to obtain maximum intensity on the detector. The GRD7 filament currents were measured in the range of 1.7- 2.2A at 750nm. Results Table of filament temperature measurements at each current Current (A) Temperature (k) 1.7 1673 1.8 1723 1.9 1773 2 1823 2.1 1858 2.2 1923 (e) λ= 750 nm Current (A) Voltage (mV) 1.7 2.8 1.8 3.2 1.9 3.7 2 4.3 2.1 5 2.2 5.8 λ= 650nm Current (A) Voltage (mV) 1.7 1.7 1.8 1.8 1.9 2 2 2.2 2.1 2.45 2.2 2.75 After plotting the tables the curves should look like this Y axis =u (^) and x axis = Wavelength in nM Questions Planck’s law on radiation is as follows;. P shows the power per meters squared per wavelength, C shows the speed of light, l shows the wavelength, h is the Planck’s constant, K shows the Boltzmann constant and T represents temperature (Greiner, 2001). This mathematical expression is used to plot the black body curves for every temperature by calculating the power or energy given out/ emitted at each wavelength. Equation 2 can be derived from equation 1 as follows: Where and the number of photon states in an energy range is seen to be given by: Therefore; From this we can show the equation from which the maximum in black body is seen And Where Finding ^max for T= 2000K ^max=1/5(hc/k) 1/T for T=2000 ^max=1/5(6.55 x 10-34 x 1/1.3806504(24) × 10−23) 1/2000 =4.744^-15 In our experiment it was preferable to work at a fixed wavelength and varying temperature the maximum wavelength emitted by a black body radiator is infinite but an object can emit a definite amount of energy at every wavelength. Therefore it would be easier to draw curves at a fixed wavelength and different temperatures for easier compilation and conclusion. Values of hc/k and h/k From the first graph T=1795.5K. From equation 3, h/k=5T750/c which is 5 x 1795.5x 750/ 299,792,456.2 = 0.0225 The value of  If an object is subjected to heat of about 1500 degrees a dull red glow is observed and therefore that object is said to be red hot. On the other hand if the same object is heated to about 5000 degrees it develops a white glow and we say the object is white hot. Experimentally it has been shown that the emissive power over the absorption coefficient is the same as a certain wavelength function. Therefore we can conclude that the value of a wavelength is essential in considering plates in thermal equilibriums. Variation in the Response of the Photodetector with Wavelength This usually is the case because as the temperature decreases, the black body radiation curve’s peak moves to intensities that are much lower and longer wavelengths. At room temperature, infra red wavelengths are usually produced by black bodies. As the temperature increases, visible wavelengths are produced ranging from red to blue. Irregularity and temperature variation along the wire An irregular cathode wire is not an ideal surface for a black body radiation to take place. This is because its geometrical and chemical compositions determine its black body radiation behaviour. This irregularity will therefore cause the cathode wire to emit less radiation from a black body. Assumptions about similarity of tungsten wire to black bodies Tungsten is not a real blackbody mainly because the total emitted radiation is less than that produced by an ideal black body. However it is a better emitter in the visible, shorter wavelength region than in longer wavelengths just like an ideal blackbody. Discussion There are three basic methods that transfer heat and radiation is one of them. The other two include conduction and convection. A hot plate may show no sign of the heat in the form of a glow but when a hand is held over it the heat could be felt. A temperature of more than 1000K is required to make an object glow. At this temperature and above might glow red and the sensation of heat will increase considerably. A bright white light is emitted if a tungsten wire is used as the filament by submitting it to resistant heating at temperatures of about 2800K. Various laws are used to represent the energy distribution of the heat radiation of a blackbody mathematically. One of the most common of these laws is the Planck’s radiation law. This law was formulated by Max Planck in the twentieth century. Conclusion There are inadequacies in experiments and theories concerning black body radiation for example the Raleigh- Jeans formula has failed horribly in predicting the actual results of experiments. This is because the radiance given in this equation is usually inversely proportional to the fourth power of the wavelength and this usually indicates that the radiance will approach infinity at short wavelengths. This short coming is referred to as the ultra violet catastrophe (Baggott, 2004). The peak of a black body radiation curve moves to the lower intensities and longer wavelengths as the temperature decreases. This curve can and is usually compared to the classical model of Raleigh- Jeans. A thermodynamic equilibrium of the state of light can be established experimentally in a rigid walled cavity that contains a black body as steady state equilibrium. A cavity without a black body object can not sustain radiation at equilibrium. The study of black body radiation therefore can be used to reveal how continuous fields of molecules and atoms can have temperature. References Baggott, J. E. (2004). Beyond measure: modern physics, philosophy, and the meaning of quantum theory. London: Oxford University Press Greiner, W. (2001). Quantum mechanics: an introduction. vol. 1. Chicago: Springer. Read More

To some extend the radiation given out by a heated body depends on the body being heated. Different objects absorb radiation differently some do not seem to absorb radiation at all like glass. These objects show that much difference when it comes to radiation absorption because there are charges in different objects that can oscillate to respond to an oscillating electric field applied externally. Apparatus Optical pyrometer (Leeds and Northrup Model 8627) GRD7 Thermionic Diode and associated power supply Direct Reading Wavelength Spectrometer Thorlabs Photodetector, Digital Multimeters, Mercury Spectral Lamp Procedure The GRD7’s tungsten filament was used as the emitting surface.

The apparent temperature of the filament was determined as a function of a heating current by the use of the optical pyrometer. The spectrometer calibration was checked before measuring the light intensity emitted by the filament. The properties of the spectrometer were also considered. These properties are used to determine the wavelength band which is passed to the light detector. Measurements of ITas a function of T were made for at least two wavelengths and the quantity hc/k was obtained from the experimental results recorded.

Calibration of Filament Temperature The pyrometer was used to obtain a calibration table relating the GRD7 filament current to the apparent temperature of the black box. The filament was observed through a hole in the central anode. The filament’s current was observed and monitored in the range 1.7- 2.2. Temperature measurements were made at each current setting so as to obtain an estimate of reliable results. Calibrating the Spectrometer The spectrometer was set up and the mercury spectrum examined.

The calibration was also checked against the mercury spectrum’s standard lines and adjusted appropriately using the green line. Slit Widths of the Spectrometer The effect of the source slit and the width of the detector slit width on the band- pass characteristics of the spectrometer were investigated using the mercury spectrum. The source slit was set up so that it could pass a bandwidth of 10nm and then the blades were also set to form the detector slit to pass the same bandwidth of 10nm.

Setting up the Detector The photo cathodes used for releasing photoelectrons, the dynodes used for multiplying the electrons produced and the anode used for collecting the current pulse are the three most important elements of a photomultiplier tube. Each of these elements must be placed at a successfully higher potential for the electrons to pass from the dynodes to the anodes for their successful collection. For the experiment a Thorlabs solid state detector was used. The eyepiece was removed and replaced with the said detector.

The detector’s output voltage was monitored using a DMM. Measuring of the Intensities] The Hg lamp was removed and the GRD7 set up so that the cathode wire was parallel to the slit of the spectrometer. The spectrum was placed centrally and the eyepiece replaced with the photo detector. The position of the GRD7 was adjusted so as to obtain maximum intensity on the detector. The GRD7 filament currents were measured in the range of 1.7- 2.2A at 750nm. Results Table of filament temperature measurements at each current Current (A) Temperature (k) 1.7 1673 1.8 1723 1.

9 1773 2 1823 2.1 1858 2.2 1923 (e) λ= 750 nm Current (A) Voltage (mV) 1.7 2.8 1.8 3.2 1.9 3.7 2 4.3 2.1 5 2.2 5.8 λ= 650nm Current (A) Voltage (mV) 1.7 1.7 1.8 1.8 1.9 2 2 2.2 2.1 2.45 2.2 2.75 After plotting the tables the curves should look like this Y axis =u (^) and x axis = Wavelength in nM Questions Planck’s law on radiation is as follows;. P shows the power per meters squared per wavelength, C shows the speed of light, l shows the wavelength, h is the Planck’s constant, K shows the Boltzmann constant and T represents temperature (Greiner, 2001).

This mathematical expression is used to plot the black body curves for every temperature by calculating the power or energy given out/ emitted at each wavelength.

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