This may be a good place for introducing new quantities and notations. An electromagnetic wave of wavelength λ (lambda, small Greek L) covers a distance of c meters each second, where c is the velocity of light in space, close to 300,000,000 meters/second. Its frequency ν (nu, small Greek N)--the number of up-and-down oscillations per second--is also the number of wave crests in that distance, and is therefore obtained by dividing c with the wavelength:
ν = c/ λ
A basic quantum law then states that the energy E in joules of a photon of light of frequency
E = hν
where h = 6.624 10-34joule-sec is "Planck's constant", a universal constant that is fundamental to all quantum theory. It was introduced in 1900 by Max Planck, when he tried to explain the "black body" distribution of wavelengths in the light emitted by a solid hot object. Incidentally, it was the above formula, published by Albert Einstein in 1905, that later earned him the Nobel prize, not (as many still believe) his theory of relativity.
Wavelength and Energy
Quantum physics is a huge subject, too big and too mathematical to cover here. It is only brought up because of its claim that the amount of energy which an atom can receive from an electromagnetic wave--its photon--depends only on that wave's length.
The process also works the other way around: when "excited" atoms give up their excess energy to an electromagnetic wave (energy they might have received, say, through a collision with some fast atom in a glowing gas) they can only do so in photon-sized amounts. The fact that atomic emissions appear in narrowly defined "spectral lines" suggests that "excited" atoms cannot contain extra energy in arbitrary amounts, but must be in one of their "energy levels" which resonate with their structure, each associated with a precisely defined amount of energy.
Each atom also has a "ground state, " its lowest energy level and the one in which it prefers to stay. When it descends from some excited state to the ground state, the starting and final energies of the atom are precisely specified energy levels. The energy emitted, equal to the difference between the two, is thus narrowly defined, producing a photon with a precise wavelength. The great success of quantum mechanics has been its ability to calculate and predict the energy levels of various atoms and combinations of atoms.
The formula E = h ν = hc/λ
means that the shorter the wavelength λ, the more energetic the photon. A photon of UV contains more energy than one of visible light, and photons of X-rays and γ-rays (gamma rays) are more energetic still. One therefore expects that hotter regions of the Sun, where individual particles have more energy, will emit electromagnetic radiation of shorter wavelength, and that is indeed observed.
The temperature of a gas is proportional to the average energy of each of its particles (the formula, by the way, is E = 3/2 kT, where T is the absolute temperature in degrees Kelvin--like Celsius, just different zero point--and k is a fixed number, "Boltzmann's constant."). Thus while the photosphere emits mainly visible light, the hot corona is better observed in EUV (extreme UV) or in long-wavelength X-rays. Flares give even higher energies to ions and electrons, and to trace locations where those particles are produced and absorbed, shorter X-rays and γ-rays are needed. All these ranges have been observed by instruments aboard spacecraft. They cannot be studied from the ground, because all short-wavelength photons are easily absorbed by the atmosphere and do not reach ground level.
An Experiment on the Photoelectric Effect
Einstein's relation suggests red photons have less energy than green ones, which have less than blue and UV ones. Frequently a photon of higher energy can initiate a chemical process which one of lower energy fails to do. Orthochromatic film (for black-and-white, the original one used) is not sensitive to deep red, so darkrooms handling film or paper with orthochromatic emulsions may have a deep-red "safelight" which helps the photographers' work but does not register on the film.
An experiment demonstrating this color sensitivity was described by Michael Horton on PHYSHARE, a web listserver for physics teacher. In his words:
I saw an excellent activity to show ... We took the green
phosphorescent paper that glows in the dark and turned off all of the
lights. We used a little pen flashlight to draw shapes on it and it glowed.
Then we used a blue light (they're pretty easy to find at auto parts stores
for keychains) and it glowed. Then we took a red laser and tried it and . .
. nothing. No matter how long you held it there or how bright the laser
was, it wouldn't glow because the light wasn't energetic enough. It was a
fun activity that taught a good lesson. I bought some of the glow-in-the-
dark paper for this year along with some white, blue, yellow, and red
lights. We'll see how it works with the students.
Chem/Phys/Comp. Repair teacher/Dept. Chair
Perris High School; Perris, CA
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