Lecture 2
Kirchhoff's Laws & Cavity Radiation
I. Kirchhoff's Laws: The Interaction of Light and Matter
A. the term "line spectra" comes from a common design of spectrographs
in which the entrance aperture (located at the focal plane of a telescope
or lens) had the shape of a narrow slit; the spectrograph optics projected
the image of the entrance slit through a dispersing element (prism or diffraction
grating) onto a screen or photographic plate such that the location of
the slit image along the screen or plate was a function of the wavelength
of the image
1. the spectra of material which radiated discrete wavelengths (colors)
resembled a pattern of different color lines on the screen or plate
2. the spectra of material which radiated continuous spectra, but
with discrete wavelengths (colors) absorbed out resembled a rainbow band
of colors with a pattern of dark lines on the screen or plate
B. Kirchhoff's laws: a set of empirical laws describing the
three main types of spectra and the state or physical characteristics of
the matter that radiates those spectra
1. Kirchhoff's law: A continuous spectrum (thermal) is emitted
from a hot solid or a hot dense fluid. (note that a relatively low
density hot, opaque plasma (ionized gas) may also emit a continuous thermal
spectrum but this had not been observed at the time)
a. continuous spectra: light (E&M radiation) radiated over
a continuous range of wavelengths
b. two main types of continuous spectra: thermal and nonthermal
- Kirchhoff's laws describe the continuous spectrum of thermal radiation
2. Kirchhoff's law: An emission line (bright line) spectrum
is emitted from a "hot" low density (low pressure) gas
3. Kirchhoff's law: An absorption line (dark line) spectrum
is seen when observing a continuous spectrum which passes through a "cool"
(cooler than the continuous spectrum emitter) low density (low pressure)
gas
C. Another important characteristic of the line spectra of the elements
was that the pattern of lines that was radiated or absorbed was unique
to that element, in this was the spectrum of a material could be used to
identify the composition of that material (the unique pattern of lines
is sometimes referred to as the "fingerprint" of the element)
II. Cavity Radiation = Black Body Radiation
A. All objects emit E&M radiation due to their temperature, a
perfect thermal radiator would also be a perfect absorber; a cold perfect
thermal radiator would perfectly absorb all wavelengths and thus would
be "black" to the eye, hence the term black body radiator = perfect
or ideal thermal radiator
B. The closest set-up in the lab to a perfect absorber is a small
hole which extends into an irregular cavity in a metal material;
since the "hole" is a perfect absorber, if the metal is heated, the radiation
spectrum that is emitted from the hole will closely approximate a perfect
thermal continuous spectrum = black body spectrum; this was also known
as cavity radiation
1. spectral observations of cavity or black body radiation determined
several characteristics which depended solely on the absolute temperature
a. cavity or black body radiation is continuous over the entire E&M
spectrum starting with zero intensity at zero wavelength, rising to a peak
intensity, then the intensity approaches zero again as the wavelength approaches
infinity
b. the wavelength at which the peak in the spectrum occurs is inversly
proportional to the absolute temperature, and the total power per unit
area emitted (the intensity summed over the entire spectrum) is directly
proportional to the absolute temperature to the forth power
c. definition of absolute temperature: the temperature
of a material is directly related to the average energy of motion (kinetic
energy) per particle in a material; if we imagine cooling a material down
to lower and lower temperatures, then the average kinetic energy per particle
would become less and less; now imagine cooling the material to such a
low temperature that the average kinetic energy per particle is zero,
this would be the lowest possible temperature of the material (for that
matter, of any material); any temperature scale which begins at this lowest
possible temperature is known as an absolute temperature scale
i. absolute zero = the lowest possible temperature of
any material = -273.15oCelsius
ii. Kelvin temperature scale = SI or metric absolute temperature
scale; uses the same scale divisions as Celsius scale but begins at absolute
zero (0 K = -273.15oC); conversion: T (K) = T (oC)
+ 273.15 (note that the correct terminology is to say just "100 Kelvin"
rather than "100 degrees Kelvin")
2. Wien's law: describes the temperature dependance of the
wavelength of the peak in the black body spectrum
lmax
= constant/T
{lmax (lambda-max) = wavelength
of the intensity peak in nm (nanometers = 10-9 meter);
constant = 2.9 x 106nm K; T = absolute temperature of
black body in K (Kelvin)}
3. Stefan-Boltzmann law: describes the temperature dependance
of the total radiated power per unit area of the black body (intensity
summed over the entire E&M spectrum)
P/A = sT4
{P/A = total radiated power per unit area in W/m2 (watts
per square meter); T = absolute temperature of black body in K
(Kelvin); s
= Stefan-Boltzmann constant = 5.7 x 10-8 W/(m2K4)}