Absolutely Small - Michael D. Fayer [52]
In Chapter 4, black body radiation was briefly discussed. A hot object gives off light. A fairly hot piece of metal will glow red. This can be seen in the wire elements of an electric space heater or an electric stove. As the temperature is increased the color will move toward the blue. It was mentioned that stars are well described as black bodies, and the color of a star can be used to determine its temperature. Planck developed a formula that yields the black body spectrum for a given temperature. Figure 9.1 shows the solar spectrum calculated using Planck’s formula that is the closest to the experimentally measured solar spectrum. The frequency is plotted in wave numbers (cm-1). Multiplying the frequency in cm-1 by the speed of light in centimeters per second (3×1010 cm/s) gives the frequency in Hz, the conventional frequency units. The top axis in Figure 9.1 is the wavelength in nanometers (nm). 500 nm is green light. 400 nm is very blue light. 666 nm is very red light. 333 nm is in the ultraviolet region of the optical spectrum and cannot be seen with the eye. 1000 nm is in the infrared part of the spectrum and also cannot be seen with the eye. These wavelengths can be detected with electronic photodetectors. Originally, they were detected with photographic film. The vertical axis is the irradiance. It is the number of watts (joules per second) that would fall on an area of a square meter in a little slice of frequency 1 cm-1 wide. Basically the plot is the amount of energy per second of a particular color that falls on a square meter.
FIGURE 9.1. The black body spectrum of the sun calculated using the Planck formula for black body radiation from a hot object. The curve is a good representation of the solar spectrum without some of the fine details. The lower axis is the frequency in wave numbers (see text). The top axis is the wave length in nanometers. The green light is 500 nm. Very blue is 400 nm; very red is 666 nm. The vertical axis is the amount of light (see text).
The shape of the spectrum plotted in Figure 9.1 is almost identical to the actual solar spectrum. The calculated spectrum is obtained by adjusting the temperature in Planck’s formula until the best match is obtained to the experimental spectrum. The temperature that gives the best spectrum is 5780 K, where K is the unit of temperature in degrees Kelvin. This is the unit of absolute temperature developed by William Thomson, the first Baron Kelvin (Lord Kelvin, 1824-1907). The Kelvin scale is used in physics and chemistry because it has a well-developed physical meaning for 0 K, the absolute zero of temperature. At 0 K, all atomic motions associated with kinetic energy (heat), the energy of moving particles, stop. To obtain the temperature in degrees centigrade (C) subtract 273. Then in centigrade, the sun’s temperature is 5507 C. To convert to Fahrenheit (F), multiply by 9/5 and add 32 to the temperature in centigrade. Therefore, the surface temperature of the sun is 9945 F. The Fahrenheit temperature scale is named for Daniel Gabriel Fahrenheit (1686-1736).
Dark Lines in the Solar Spectrum
It is remarkable that the Planck formula developed using the first quantum concept, that the energies of electrons “oscillating” in a metal are not continuous, can be used to determine the temperature of stars. The calculated spectrum shown in Figure 9.1 is continuous because a hot object produces a continuous distribution of colors (energies of light). While the experimental measurement has the shape shown in Figure 9.1, it also has some very sharp features in it that are not part of the sun’s black body spectrum. Figure 9.2 is an illustration of the solar spectrum with thin dark lines that represent a lack of light at certain frequencies. The spectrum shown in